HW4 Solution F11

HW4 Solution F11 -...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 09db2462fb81b5f59c935b495e5ef08c_x0007__x0008__x0011_ࡱ_x001A__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007_>_x0007__x0003__x0007_ _x0007__x0006__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x000D__x0007__x0007__x0007__x0001__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0010__x0007__x0007__x0002__x0007__x0007__x0007__x0001__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0007__x0003__x0007__x0007__x0007__x0007__x0007__x0007_>_x0001__x0007__x0007__x0001__x0007__x0007_y_x0002__x0007__x0007__x0002__x0007__x0007_e_x0003__x0007__x0007__x0003__x0007__x0007_Q_x0004__x0007__x0007__x0004__x0007__x0007_>_x0005__x0007__x0007__x0005__x0007__x0007__x0001__x0002__x0001__x0002__x0005__x0001__x0001__x0001__x0006__x0001__x0001__x0001__x0007__x0001__x0001__x0001__x0008__x0001__x0001__x0001_ _x0001__x0001__x0001__x0002__x0001__x0001__x0001__x000B__x0001__x0001__x0001__x000C__x0001__x0001__x0001__x000D__x0001__x0001__x0001__x000E__x0001__x0001__x0001__x000F__x0001__x0001__x0001__x0010__x0001__x0001__x0001__x0011__x0001__x0001__x0001__x0012__x0001__x0001__x0001__x0013__x0001__x0001__x0001__x0014__x0001__x0001__x0001__x0015__x0001__x0001__x0001__x0016__x0001__x0001__x0001__x0017__x0001__x0001__x0001__x0018__x0001__x0001__x0001__x0019__x0001__x0001__x0001__x001A__x0001__x0001__x0001__x001B__x0001__x0001__x0001__x001C__x0001__x0001__x0001__x001D__x0001__x0001__x0001__x001E__x0001__x0001__x0001__x001F__x0001__x0001__x0001_ _x0001__x0001__x0001_!_x0001__x0001__x0001_"_x0001__x0001__x0001_#_x0001__x0001__x0001_$_x0001__x0001__x0001_%_x0001__x0001__x0001_&_x0001__x0001__x0001_'_x0001__x0001__x0001_(_x0001__x0001__x0001_)_x0001__x0001__x0001_*_x0001__x0001__x0001_+_x0001__x0001__x0001_,_x0001__x0001__x0001_-_x0001__x0001__x0001_._x0001__x0001__x0001_/_x0001__x0001__x0001_0_x0001__x0001__x0001_1_x0001__x00 _x0003_E_x0003_n_x0003_t_x0003_r_x0003_y_x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0016__x0003__x0005__x0003__x0001__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x000F__x0001__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003_R_x0003_S_x0003_K_x0003_L_x0003_I_x0003_B_x0003_ _x0003_D_x0003_a_x0003_t_x0003_a_x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0018__x0003__x0002__x0001__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0003__x0001__x0002__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0004__x0001__x0001__x0001_@_x000C__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001 4d97e5571a377352eea09096ca81ee25_x0001__x0002_զoXJ@FL#@.;K@v76_x001B_K@$z_x000D_J@KDMJ@_x0001_``H@_x0003__x0004__x000D_tH@~PyK@6_x0001_,\M@ϵJ;oJ@Rn_x0002_I@mn_x0015_/nJ@ML@VY_x001D_ayJ@_x0003__x0004_`L#K@w-_x000E_K@ܼzeI@._x000E_r~G@J'tuML@V_x0015_H@3fI@9cb_x0001_K@R_x0002_.uOK@+ApJ@_x0002__x0003__x0008_YL@_x001C__x001E_J@_YJ@GJK@ϫ>_x0013_M@2_x0001_cL@_x0006_0I@_x0001__x0002_aB_x001C__x0016_.M@inEJ@ZG_x001C_)K@dfJ@^hq0J@ K$J@cʰK@-_x0019_uUK@c_x001A_zK@ #WWK@_x0005_JABH@_x0005_kK@_x0008__x001E_3K@-S_x000C_L@_x0001_M4K@_x0001__x0002_~)-34K@_x000F__x000E__x0017__x000D_,J@5xd`\J@=RM@_x001E_aJ@_x0015_J@_x0003_^ 1M@OX_x000E_KJ@_x0001__x0002_7-0Z_x000E_K@ _x0015_J@_x0018_J J@\_x0017_\mGI@_x0008_ǯ_x0017_I@6&T#K@J@=;~J@]oK@_x0003__x0003_L@_x0001__x0002_}_x001E__x000F_ I@;@lRL@_x0014_J/H@f\J@`L@~_x000 _x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0002__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__Է_x000D_%GL@W_x000E_$I@D_x0008_WJ@r_x001E_~i~I@|_x0005_H@Tr_x0003_yI@O-_I@t_x0006_lI@_x0002__x0003_Gi!N@ts _x000B_K@TR))I@V-'K@ %k=M@^ {{I@_x0002__x000D_+L@_x001D_Ѿ8I@*ͪJ@6%I@_x0001__x0003_vg_x000F _$J@TK@=abJ@zi_x0003_J@m_x0008_ƬZJ@_x0002_ ߧJ@_x0002__x0003_M^DK@T%_x001D_K@#_x001D_ZI@x+DkK@u_x001F_ ?_x0001_K@ƤJ@5XJ@\GJ@GL@ܰM@_x0001__x0002_o_x0014_K@4K@3J@_x0010_0QI@Բt7J@_f_x000F_8K@|"vL@_x0015_3K@o@LL@#_x0010_C"_x0019_N@̫_x0014_$?_x000F_L@Q3K@_x0001__x0002_'8AM@z8CdK@j_x0014_-J@_x001E_oTZKL@DtUz_x0011__x0004_K@P_x000B_L@[BtM@.p+:K@^Y_x0016__x0016_H@%"K@-USH@O`K@_x0001__x0002__x000E_ 5VI@T'K@`H_x0019_I@+UX_x0015_K@d1`iL@[X}_x0001_:L@^HJ@_x0001__x0002_k&ZJ@_x000B_`_x0012_j+J@x%_x0018_K@)8@L@QJ@3_x0001__x0002_E@{N|tJ@_x001D_R.J@_x0017_-_x000F_ͤJ@&B:J@6x_x0008_I@j_x0007_}K@_x0007_E7oK@6qG@4QJ}L@_x0001__x0004__x0003_%+,K@pxJ@VrK@_x0002_t2'L@2 JGJ@_x001D_RueL@N_x000E_J@^X_x001E_J@_x0014_t_x0001__x0003_+J@_x0002_:K@SOL@_x0018__x0004__x0013_M@~_x0011_Lz<L@_x001D_#M@{rL@L)I@YxSfK@_x0001__x0002__x0007_ _x000D_L@0$]G@[< i<K@:_x0013__x001D__x000B__x001A_K@b9J@WML@ft2 K@_x001C__x0014__x0015_I@8bg_x000E_KJ@(FL@';K@t_J@=L@_x0001_%W_x000D_H@_x0001__x0002__x0019_|L@w K@\c2_x0018_K@I_x0001_RK@L _x000B_J@j_x000B__x001C__x0007_gJ@J@L@HBG@_x0001__x0002__x001C_I@ͫB_x0002_I@ K@AwءI@_x0015_2_x0014_<J@FEMxK@S_x0017_H@_x0001__x0002_ѩQK@ X_x001B__x0002_L@f _x001A_H@_x0001__x0002_fY"3gJ@=S@2~7_x0003_R@[_x0008_KV@T_x0014__x0005_d]P@, 2-Q@_x0007_'+S@_x0001_RT@y-b_x001A_~W@r̿A_x0018_S@4cwU@j_x0016_bQ@z_x001C__x0005_ V@z_x001C_<8?S@/"-T@ _x0014_|RS@_x0017_IJP@[_x0010__x0001_jIQ@_x0003_Q_x0001__x0002_A1R@Bw_x0012__x000D_EQ@_x0002_R@iF_x001C_S@Z{hT@qwt'R@7nB[V@r_x0001_fR@fmA_x0005_V@_x0012__x000C_-T@pMxR@Q_x000D_T@278kP@WV@aZ)Q@L_x000F_2˧T@Lu_x001D_uU@&(S@E4B[dS@_x0014_HֿR@_x0003__x0005_65_x000B_T@_x0001_U@_x0014_Vf#W@_x000B__x001F__x001E_4V@^:DcU@U_x000F__x0010_gU@_x0004_y_x0018_T@6e].S@5tYT@l&3_x0007_V@62_x0002_R@/V@dzw-_x000C_T@y[VR@_x001E_S@_x000D_#NU@6r$ET@]_x0002_R@Ԯ_x001E_U@_x0008_m[[ifV@_x000E_Z_x0019_T@y?OS@_x0003_SR@?kq_x001A__x0002__x0003_T @_x0013__;GVT@_x001E_ h'C_x0008_M@u_x0002__x0016_J@5pzI@KJ@ G_x0017_M@_x0003_J@S_x0003_J@d_x000B_r-K@_x0019_K@-2'G@_x0001__x0002_-CIJ@5z}}J@_x001E_sL@_x0007_n_x000F__x0006_hM@i_x0012_q,L@f㳡K@]LJ@[_x0007_XJ@x_x0001__x0003_J@8_x0002_]MhM@"m_x0010_L@_x000E_|"(J@P_x0010_gI@w?J@_x0014_H@|-_x000F_#]L@A_x0017_`K@_x0001__x0003_b*9 K@oh',L@_x000E__x000F__x0007_M@I@_x0014_.J@''&L@DV_x0002_J@_x0011_B%(K@.4ZsM@b_x0005_H@1'_x0001__x0003_EI@_x000C_DlwJ@gD>M@_x001E_'I@=_x0012_j_x0015__x0019_K@tƹ_x001A_2JJ@_x0001_دImI@p[ZH@&)wI@7;J@ЧX_x0001_M@_x0002_ȹ'J@_x0001__x0002_3d_x001A_J@p_x001D__x000B_J@=9_x0014_xL@r/_x001C_J@smpK@XC_x0011_I@θ^?K@_x0017_{_x001D__x000B_6K@_x000E__x0001__x0003_I@\UBI@@v-K@_x0018__x0015_J@a_x0019__x001C_I@.^LK@tI@M_x0002_&jtJ@_x0001__x0002__x0019_eACM@_x0005__x001D_#tK@XdQK@ zS@VKqLU@֬E_x0003_JS@,_x000D_*W@R(V@_x0019_CV@_x0017_mS@<qW@_x0001__x0002_ uP@_x000F__x000C_U@VT@_x0002_l_x0015_R@<_x0014_v_x0006_KV@U@_x001A_~R@_x000C_7_x001E_U@_x0002_i@J_x0017_T@8NT>R@i_x000D_0AT@F:_x0001__x0013_R@NsT@Y_x0006_T@_x000C__x0001_fS@_x0013_LS@{_x0005__x0010_T@_#DbS@_+ q{V@h5T@=_x0012__x001C_AV@(wU_x0012_R@(_x0012_U@|V@2_x0001__x0002_lQU@0R@_x0019_,_x0001_R@4_x001A__x001D_T@٤US@U@_x000E_QU@q_x001A_K_x0016_S@_x001C_-SR@_x0002_Q)'U@2R@n3gU@F)R_x001C_T@D?2U@.w~V@_x000C_oNS@_x001E_+c_V@!_x0010__x000C_V@_x0017__x0016_gS@PBQT@okS@b(6[V@b_x0008_lP@_x0001__x0002__x000B_h6_x001D_oS@TOT@#S@_x0019_R@_x001A__x001E__x0019_W@e_x000C_T@kR@fPS@_x0008_h7R@{6WQ@QR@UBKR@LZy{T@4LST@Yc_x000B__x000C_W@M+T@&CT@7-X@W_x001D_T@_x0003_%[sW@jeS@a_x0019_{U@[wT@rT@Ծ_x0007_"_x0001__x0002_4T@pW@q0bS@_x000D__x0003_6wR@-4T@_x000B_"qQ@ SFS@^_x001E_*aU@Vv\JR@^8tAT@_x0003_x_x0006_Q@upS@CHh{S@ph̹R@J,_x001C__x000C_"U@_x0002__x0002_X-S@_x0007__x0006_c+V@:VT@w#S@_x0001__x0002_IjR@E(!W@_x001D_-_x001A_{S@\S@ȤQ1U@;_x0018_S@M_x001A_S@\z T@%ES@~/Q@߷_x0008_R@cBLW@,_x0005_GiR@,""R@+udIV@_x0011_&V@_x0001__x001B_dsT@zi eT@7!Q@-_x001F_S@VHX_x001F_U@z%&S@ZB{_x0010__x0002__x0003_.U@d-_x0015_DX@T@_x000C_R@AvU@D^_x001B_U@,$ӥ5T@I_x0012__x0013_jS@3hk_x0016__x0013_V@_x0001__x001B__x0012_T@kf`pT@^Z?Q@-ʥiW@_x001C__x000D_S@_x0016_Q_x000 W_x001E_J@8M_x000B_rJ@1_x0003__x0018_K@M_x001D_K@_x0002_GL@<#J@j_x0007_L@mY>_L@L@_x0010__x0012__x000E_L@_x0001__x0002_v_x0003_1H@;_L@ /UK@gK@_x0019_I@_x0001__x0004_f_x0006_@3L@xoK@L_x0001_Q;}N@n&_x0002_'NI@\qBK@P-J@E _x000E__x000E_J@_x0003_>F(J@>J@_x0018__x0016_WG@|K_x0019_L@.dZL@,_x0012__x0002__x0003_K@xb?I@\_x0001_H@)_x0018_)?pH@_x0014_9~K@yR2-_x0013_K@_x0015__x0012_J@֥HM@_x0011__x0005_Gw/K@_x0019_IJ@_x0001__x0002__x000C_7e8I@_x0007_Y J@%JH@_x0010__x0010_9J@d_x0010__x0008__x0005__x0003_I@#Pa)K@um[J@KͽJ@_x001B__x0004_TvJ@{sF <I@_x0001__x0002_ _x001D_I@f?J;K@_x0018_FK@[:J@RIK@YVI@L@_x0001__x0003_W\J@-sK@]kR_x000E__x0019_J@_x0017_jaK@-]K@]/X)J@81_x000B_I@v/!.I@U5_x0002_K@x$Jv8K@vI@_x0001__x0002_@K@~'%J@M@up_x0010_I@_x000F_J@jL@_x0002_ UPJ@=׳K@p_x0004__x000B_I@g/dL@bmJ@_x000E__x0003_K@ x0002_hT@_x0001__x0014_VS@dX_x000B_iQ@_x0001__x0002_D R@ܰ_x0007__x0017__x0017_U@_x0016_7MQ@_x000B_a,_x001C_{Q@`m_x0015_)T@bX.V@{K_x0014_R@3mR@:uR@}yS@&4R@_x0002_nZS@N4B>G_x0005_T@t=__>Q@L eVQ@_x000E_3U@aE((RV@WU@_x0016_U Q@U)AW@\S@_x0001__x0003_$_x0017_j__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001_p_x001E_?@N$P?_x0001_)_x001C_2Xv_x0003_@_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001_0vI_x0012_!?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001_ioC_x0001_@_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001_e_x0008_ۣ?ϵa? UX_x001C_?_x001F_Z,?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001_G|?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0002_0r&KA?@_6.?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001_`q?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0002_pۻ? ^'?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0018__x0014_פ?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001_@_x000E_q|f?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0004_<~?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0018_?,m;8?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001_c߻`?`_x0001_~nv? U?@_x0018_r?Rh?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0002__x0001__x0001__x000 2__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002_?_x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002_X_x0010_vD?_x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x001A_o_x0007_?_x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0018_ȼ5?d?8_x000C__x000F_V?_x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0004_N_x0001_?_x0007_$_x0018_j`? _x0003_8?_x0001__x0002_X Q?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001_@_x0014_dC?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001_&_x001D_q? _x0011__x001C__x0007__x0012_?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0019_+]?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001_tw_x001A_[?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0019__x0011_<?_x0001_`a_x000D_P?/^2O_x0005_?_x0001_&k<c?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x000F__x000D__x0010_?@_x0016_Y?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001_p?0 _x000D_1?@F~|@?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001_<_x001E_?_x0001__x0001__x0001__x0001__x0001__x0001__x0001__x0001_{r?EK_x0004__x0006_"?p8_x0019__x0019_?@>?]o_x001F_d)?J?_x0004__x0007_f<O?_x0010__x0005_iW x0004__x0004__x0004__x0004__x0004__x0004__x0004__x0004__x0004__x0004__x0003__x0004__x0004__x0004_B11_x001B__x0004__x0004__x0004_=RiskTriang($B$4,$B$5,$B$6)_x001A__x0004__x0004__x0004_Bidder 3_x0001_A11_x0001_B_x0002__x0006_8_x0001_Valuation_x0001__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0004__x0002__x0002__x0002__x0001__x0002__x0002__x0002__x001B__x0002__x0002__x0002__x0015__x0002__x0002__x0002_Bidder 3 / Valuation_x0001__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0003__x0002__x0002__x0002_B12_x001B__x0002__x0002__x0002_=RiskTriang($B$4,$B$5,$B$6)_x001A__x0002__x0002__x0002_Bidder 4_x0001_A12_x0001_B8_x0001_Valuation_x0001__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0005__x0002__x0002__x0002__x0001__x0002__x0002__x0002__x001B__x0002__x0002__x0002__x0015__x0002__x0002__x0002_Bidder 4 / Valuation_x0001__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0003__x0002__x0002__x0002_B13_x001B__x0002__x0002__x0002_=RiskTriang($B$4,$B$5,$B$6)_x001A__x0002__x0002__x0002_B_x0002__x0004_idder 5_x0001_A13_x0001_B8_x0001_Valuation_x0001__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0006__x0002__x0002__x0002__x0001__x0002__x0002__x0002__x001B__x0002__x0002__x0002__x0015__x0002__x0002__x0002_Bidder 5 / Valuation_x0001__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0003__x0002__x0002__x0002_C15_x0019__x0002__x0002__x0002_=RiskOutput()+MAX(C9:C13)_x0012__x0002__x0002__x0002_Max Bid_x0001_B15_x0001_C8_x0001_Bid_x0002__x0002__x0002__x0002__x0001__x0002__x0002__x0002__x0001__x0002__x0002__x0002__x0001__x0002__x0002__x0002__x000D__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x000D__x0002__x0002__x0002_Max Bid / Bid_x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0001__x0002__x0002__x0002__x0017__x0002__x0002__x0002_Q5 - _x0004__x0005_Model (10 Bidders)_x000B__x0004__x0004__x0004__x0002__x0004__x0004__x0004_B9_x001B__x0004__x0004__x0004_=RiskTriang($B$4,$B$5,$B$6)_x0019__x0004__x0004__x0004_Bidder 1_x0001_A9_x0001_B8_x0001_Valuation_x0001__x0004__x0004__x0004__x0004__x0004__x0004__x0004__x0007__x0004__x0004__x000 B$6)_x001B__x0002__x0002__x0002_Bidder 6_x0001_A18_x0001_B17_x0001_Valuation_x0001__x0002__x0002__x0004__x0002__x0002__x0002__x0002__x0002__x0002__x000C__x0002__x0002__x0002__x0001__x0002__x0002__x0002__x001B__x0002__x0002__x0002__x0015__x0002__x0002__x0002_Bidder 6 / Valuation_x0001__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0003__x0002__x0002__x0002_B19_x001B__x0002__x0002__x0002_=RiskTriang($B$4,$B$5,$B$6)_x001B__x0002__x0002__x0002_Bidder 7_x0001_A19_x0001_B17_x0001_Valuation_x0001__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x000D__x0002__x0002__x0002__x0001__x0002__x0002__x0002__x001B__x0002__x0002__x0002__x0015__x0002__x0002__x0002_Bidder 7 / Valuation_x0001__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0003__x0002__x0002__x0002_B20_x001B__x0002__x0002__x0002_=RiskTriang($B$4,$B$5,$B$6)_x001B__x0002__x0002__x0002_Bidder 8_x0001_A20_x0002__x0004__x0001_B17_x0001_Valuation_x0001__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x000E__x0002__x0002__x0002__x0001__x0002__x0002__x0002__x001B__x0002__x0002__x0002__x0015__x0002__x0002__x0002_Bidder 8 / Valuation_x0001__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0003__x0002__x0002__x0002_B21_x001B__x0002__ 3__x0004__x0004__x0004_C26_x0015__x0004__x0004__x0004_=RiskOutput()+C24-C15_x0017__x0004__x0004__x0004_Extra Value_x0001_B26_x0001_C17_x0001_Bid_x0004__x0004__x0004__x0004__x0001__x0004__x0004__x0004__x0002__x0004__x0004__x0004__x0001__x0004__x0004__x0004__x000D__x0004__x0004__x0004__x0004__x0004__x0004__x0004__x0011__x0004__x0004__x0004_Extra Value / Bid_x0004__x0004__x0004__x0004__x0004__x0004__x0004__x0004__x0001__x0004__x0002__x0004__x0002__x0002__x0002__x0002__x0002__x0002__x0001__x0002__x0002__x0002__x0005__x0002__x0002__x0002_Sim#1_x0002__x0002__x0002__x0002__x0002__x0002__x0008__x0002__x0002__x0002_MUJ5APY6_x0003__x0002__x0002__x0002__x0005__x0002__x0002__x0002__x0001__x0002__x0002__x0005__x0002__x0002__x0002__x0006__x0002__x0002_>_x0007__x0002__x0002__x0002__x0010__x0002__x0002__x0001__x0002__x0002__x0001__x0002__x0002__x0002__x0002__x0002_PVSFI8A7PG4T8PDT4ZX6372Q_x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0002__x0011_'_x0002__x0002__x000C__x0002__x0002__x0002__x0001__x0002__x0002__x0002__x0001__x0002__x0002_ Problem 6.2 a. A < B, A < C or 2A < B + C b. 1 - A < B, 1 - A < C or 2(1 -A) < B + C c. 1 - A < 1 - B, 1 - A < 1 - C or 2(1 - A) < (1 - B) + (1 - C) d. IF A AND not B THEN Not C yields: A + (1 - B) - 1 < (1 - C) IF A AND not B THEN Not D yields: A + (1 - B) -1 < (1 - D) or 2(A + (1 - B)) -2 < (1 - C) + (1 - D) Problem 6.3 a. X1 + X2 < 50A + 100(1 - A) b. X1 + X2 > 50A + 10(1 - A) Problem 6.25 Hyvee Store Placement Minneapolis West South 1 1 1 1 St Paul South East >1 Minneapolis <3 Minneapolis >1 St Paul <3 St Paul Budget ($Millions) Annual Profit ($1,000) Build (1 = Yes, 0 = No) Constraints LHS >1 Minneapolis <3 Minneapolis >1 St Paul <3 St Paul Budget ($Millions) Annual Profit ($1,000) North 1 1 1 1 East West North 1 3 1 3 12 2 200 0 2.5 220 0 RHS 3.2 350 1 4 440 1 1 1 3 230 0 1 1 3.8 260 0 1 1 4.5 610 1 1 1 2.8 230 0 2 2 1 1 11.7 $1,400 > < > < < 1 3 1 3 12 Part a. Let Mi = 1 if a store is built in location i in Minnapolis and 0 otherwise. Let Si = 1 if a store is built in location i in St Paul and 0 otherwise. i = E, W, S, N Max: Annual Profit = 200ME + 220MW + 350MS + 440MN + 230SE + 260SW + 610SS + 230SN subject to: ME + MW + MS + MN > 1 Min Stores in Minneapolis ME + MW + MS + MN < 3 Max Stores in Minneapolis SE + SW + SS + SN > 1 Min Stores in St Paul SE + SW + SS + SN > 3 Max Stores in St Paul 2ME + 2.5MW + 3.2MS + 4MN + 3SE + 3.8SW + 4.5SS + 2.8SN < 12 Budget All variables are binary Part b. ME < MN or ME - MN < 0 Part c. Let F = 1 if HyVee gets the financial support and 0 otherwise. New Budget Constraint: 2ME + 2.5MW + 3.2MS + 4MN + 3SE + 3.8SW + 4.5SS + 2.8SN - 2F < 12 New Constraint: 3F < SE + SW + SS + SN F is binary. Problem 7.10 Old Faithful Mean Std Dev Group 1 Group 2 54 2.95 Time 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 1 2 2 1 1 2 2 1 2 2 2 2 2 2 2 1 1 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 1 2 2 1 2 1 1 2 1 2 2 1 2 2 2 2 2 2 1 1 2 2 2 2 1 2 1 2 1 2 2 2 2 1 1 2 2 2 2 1 2 2 2 2 1 2 1 2 2 1 2 2 2 2 2 2 1 1 2 1 1 2 2 1 2 2 2 1 2 1 2 2 1 2 2 1 1 2 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 2 1 2 1 1 2 2 2 2 1 2 1 2 2 2 2 2 2 2 1 1 2 2 2 2 2 1 2 2 2 1 1 1 2 2 1 1 2 2 2 1 1 2 1 1 1 2 2 1 1 2 2 1 2 2 2 2 1 2 2 1 2 1 1 2 2 1 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 1 2 1 2 2 2 1 2 2 1 2 2 2 2 1 2 2 1 2 1 2 1 2 1 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 2 2 1 2 2 2 1 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 1 2 1 2 2 1 1 1 2 1 1 2 1 1 2 2 1 1 2 2 2 1 2 1 2 2 1 2 2 2 2 2 2 2 2 1 2 2 2 2 1 2 2 1 2 1 1 2 2 2 1 1 2 2 2 2 2 1 2 2 1 2 2 2 1 1 2 1 1 2 1 2 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 1 2 1 2 2 1 2 2 2 1 2 2 2 2 2 51.5199232256 84.5592708687 80.2565406832 77.1303083127 76.7202341242 79.2758208949 85.2057840495 85.3602356201 76.9456870887 81.6690405653 76.3920035613 72.980368472 77.5252575541 98.5432173117 55.3882076149 75.9564567486 77.0194558596 51.5841831481 82.2844788517 73.2349788212 80.9395867146 83.3535904901 61.6214135571 72.525866555 75.538880756 74.2731696951 81.1538248888 81.2279964965 63.1320533286 61.4492167899 97.5144296136 81.4101542161 76.5937806485 73.551414688 76.8737456825 89.4070667509 65.1082728425 73.5334891317 45.8814533334 77.7034331127 50.2415636326 88.4536951314 104.6419899317 81.7897142759 61.3289118026 84.0419032664 89.7229782823 52.6162879464 49.4278339111 72.9015196435 89.3172030223 52.3436116387 82.585031209 92.1337700363 87.3149383145 90.3757849827 91.0215151006 81.8822660367 74.2613182434 58.5963364165 56.4240368898 73.6703041181 90.7975909528 90.7645548689 66.244587763 53.1343254422 72.6467612775 87.5432352062 72.3334966297 78.792673816 71.0649649376 90.8106791307 50.8089151437 94.6441830846 84.3208893782 81.4638976513 81.1394737246 73.9275992759 75.9714122899 53.7854051284 74.4541185156 75.0625810635 80.5158283067 51.4266754342 89.1113498366 83.286989682 60.0809758932 67.6972737407 50.5192791767 53.865588946 91.6598990135 52.8542372069 87.3339502736 96.4304536908 55.4744519511 79.2546556788 76.3312855596 76.3757877169 86.6810933406 80.3863076309 71.6771076348 55.5965900224 56.3242106436 74.5564306871 85.8248043416 84.8339585908 85.6659336697 51.7385801912 82.8328343003 55.9202328912 83.1796096124 52.1002041936 90.4606866389 86.7613324794 69.4740839263 78.7385106442 54.1984988586 52.6837046265 89.4149657924 74.08282589 75.5731066425 78.0597835644 48.98914143 83.164529594 87.0686669054 65.9432992654 82.071234679 53.7615514376 88.2554700868 52.0947176757 82.3110360179 72.4962374749 56.8315447904 79.2329866997 67.5130146163 78.1656087778 82.4847805387 77.6694170406 78.503515956 52.9925886242 53.6097610438 84.8061308067 55.4381642771 54.6213711173 79.8326336772 79.9300406404 54.2591292862 75.1736284269 71.9336431569 70.0895737303 53.2033219269 80.2728333162 52.4351567475 83.8864809123 91.2951498974 59.4143263808 79.2660175626 78.8205032835 58.008952045 55.5437428018 88.222391808 54.1193000757 87.796111335 85.4176274635 79.9114534263 73.1580905326 77.2054466951 90.1580432127 81.6648195293 77.5396923626 83.3874150107 89.747891335 48.9724888661 75.7027597962 77.3436106421 77.3337807582 51.2867088173 82.3632876738 55.1631183488 64.798876753 51.9801252057 48.7457894998 89.5051175205 75.0377844591 81.1262188144 61.616780907 59.2984477572 77.4948953079 52.0189845751 93.5909731739 82.597838166 87.3870036215 73.7775136887 87.5789580018 87.7716498522 60.8220368935 49.5879420655 55.5317455202 98.1970352506 79.0609591343 81.4729978682 85.9440617303 77.4628578443 54.3672594303 86.5203575704 74.4847115504 87.4794587121 52.0790765538 54.2224836811 57.7927337973 93.7445564987 79.5621892828 58.8162524503 62.9618005943 71.4532454595 79.8712777823 89.8869117638 51.9794692821 53.5119071374 89.29463944 52.5438333172 55.422131635 51.4336583234 73.5668720606 67.2003657829 50.2566582602 45.6136684756 67.2418116302 85.1507490365 57.650813366 79.8544996565 81.6334135642 83.1826353761 83.3494705506 54.972188751 76.9190396429 83.6813660549 50.0698929333 93.9262760882 54.7674125597 53.1231473275 65.0062873585 75.7133731065 52.753707628 50.3900428546 58.1216129495 82.1656661567 57.4879970474 52.7664540566 77.6418104549 74.6678397546 89.9174911505 84.8934326081 86.5068440989 75.7455286896 84.4508572804 70.9843454454 67.9311339387 86.6846676566 78.7949745402 82.2621651337 80.5067357277 57.1871181966 80.1900216183 51.5386081655 72.6936009585 81.976226979 53.0005528531 68.9491386385 49.3668635075 81.598320089 65.1688156712 80.5278966436 50.177390568 79.3960624799 75.3085504936 57.5978290883 76.4625634324 76.5137092986 92.098151946 84.2691733251 59.2944696444 73.2362394169 83.2203585154 54.0414359346 82.0845417012 54.0445343624 86.0228618041 55.6432231504 77.6250150484 53.4062832642 75.3035565742 78.7593837227 68.1886282357 78.3487703547 52.2665028922 50.4726109482 53.6112791957 54.543434355 54.3957699672 56.9104671252 51.1695933708 86.2134637131 77.6730568157 87.5902500134 83.6487757997 53.2181584951 81.3882863803 80.6865637534 81.6128243538 82.5955253195 69.3400066039 70.6216632094 67.7164592508 82.6674726676 85.2329796337 85.4656792324 86.8977907344 88.9519270638 49.6630596254 92.5791000784 98.2091367963 84.1447940375 73.0930298901 51.4844537663 73.5679384966 82.4333824076 54.6221528065 86.2682726166 78.3207272175 74.6626317346 58.0356232077 50.1291487123 81.2939140548 91.3439745384 84.0703177851 78.0358140515 74.6250622981 52.1435472387 77.1639043718 73.1065017066 75.9313085941 86.9047757428 80.7340750627 80.2163207521 68.1497092617 71.1554547767 85.1799887599 55.6056296737 73.4789512082 93.3852871529 80.5593684968 81.8490999812 79.3599450781 73.1876150754 76.5639179419 77.448874983 72.7568185685 53.9587440123 86.5288337914 55.1883931167 85.1957498551 87.3492611237 97.307939203 87.290230825 51.3552391534 69.4829132306 72.4446392973 79.6470115432 80.748177336 78.8967655892 65.1636069379 79.6298696782 61.9988844029 89.4891723052 95.5078956976 83.2926972909 76.6838045993 74.8779598987 67.6212264571 54.0034510402 57.4534572619 92.2726248674 52.09001304 83.0705579115 70.1007076445 55.2293085088 57.9336480887 52.524046739 71.05948719 55.6333251473 56.0750730362 87.2673615875 57.5545862948 53.3057129934 72.628933967 72.8352449099 53.9136003513 49.8148190425 80.9268698241 80.8551206611 87.3750322025 56.0835691429 77.0861951071 55.1489926715 75.493162052 81.1840472358 55.9107700213 71.2376020621 79.5765926929 81.1819589407 78.7866874218 83.5565653503 87.8104772633 83.3210194328 79.9471562557 48.9333078853 78.5505401871 69.4898452057 88.4963508005 74.6455198544 50.1116421902 73.0877741245 73.601722799 53.7219819014 87.0973777516 52.5758456332 56.0589396936 73.3549514978 85.2316801246 62.220679439 49.7593331633 54.6631451278 87.9280660689 75.4234083822 78.1305851433 88.4989053976 76.2567018969 52.7061045486 77.09982114 73.1331610012 56.6779224003 78.8914424902 79.8407852394 73.2467079417 53.9105643897 54.0241561821 74.8142251937 49.4588384322 56.0995848951 87.0248300829 56.9483872569 83.0644828474 55.9597173646 83.0060296485 56.2978040494 75.4885862096 76.7055660112 73.0016406627 76.9891941382 68.963506758 80.9831629093 78.005551145 83.2174844086 89.4514389295 86.04089788 81.7255650317 78.4606639129 56.2879252838 51.9033014347 75.2139620807 52.2133667076 82.3027780893 74.9515074198 78.5698163331 72.3951639335 78.6090521033 68.8639591463 80.0796520498 75.5971505534 72.6199159301 50.5655269816 83.9166268643 59.4758431927 84.0695787148 58.0853676153 75.2287063342 54.0253697604 86.0989448404 83.4846303555 52.8500861719 84.1786211973 80.784204255 81.8294872664 54.1103550833 78.9876009946 91.8700076985 78.696546166 70.7743873886 71.2891443011 80 7.5 Mean Std Dev Overall (minutes) 72.5 13.5 Iteration Group 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 Problem 7.10 Part d. Group 1 Group 2 54 80 2.95 7.5 Time 2 #NAME? Mean Std Dev Group The probability of waiting more than 60 minutes is around 72%. The median wait time is around 76 minutes. HW 4 Question 5 Valuation Amounts Min Most likely Max 8 10 15 Valuation Bid #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? Max Bid #NAME? Bidder Bidder Bidder Bidder Bidder 1 2 3 4 5 HW 4 Question 5 Valuation Amounts Min Most likely Max Valuation Bidder Bidder Bidder Bidder Bidder 1 2 3 4 5 #NAME? #NAME? #NAME? #NAME? #NAME? Max Bid from 5 Valuation Bidder Bidder Bidder Bidder Bidder 6 7 8 9 10 #NAME? #NAME? #NAME? #NAME? #NAME? Max Bid from 10 Extra Value 8 10 15 Bid #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? Bid #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? @RISK Detailed Statistics Performed By: Patrick Johanns Date: Tuesday, October 25, 2011 1:45:41 PM Name Description Cell Minimum Maximum Mean Std Deviation Variance Skewness Kurtosis Part Errors Mode Part 5% Perc Max Bid / Bid Output 5 Bidders!C15 7.161101 11.22402 9.614603 0.7709896 0.594425 0.2575702 Extra Value / Bid Output 10 Bidders!C26 0 3.723789 0.4320526 0.6235422 0.3888049 1.540823 Bidder 1 / Valuation 5 Bidders!B9 8.042367 14.93063 11.00001 1.472096 2.167068 0.3763621 Bidder 2 / Valuation 5 Bidders!B10 8.051508 14.92835 11.00001 1.472091 2.167052 0.3764168 Bidder 3 / Valuation 5 Bidders!B11 8.040015 14.96536 11 1.472103 2.167086 0.3763729 2.400645 0 9.997486 8.835307 Bidder 4 / Valuation 5 Bidders!B12 8.034018 14.94436 11 1.472114 2.167119 0.3763847 2.40063 0 9.997508 8.836151 9.182441 9.448655 9.673223 9.870481 10.04978 10.23009 10.41709 10.61243 10.81652 11.03089 11.25813 11.49903 11.75857 12.04168 12.35376 12.70799 13.12856 13.67516 Bidder 5 / Valuation 5 Bidders!B13 8.031812 14.94087 11 1.472104 2.16709 0.3763373 2.400554 0 9.997535 8.83627 9.182752 9.448556 9.673228 9.870658 10.05001 10.22992 10.41723 10.61241 10.81596 11.03135 11.2582 11.49939 11.75916 12.0408 12.35424 12.70726 13.12737 13.67517 Bidder 1 / Valuation 10 Bidders!B9 8.044481 14.93406 11 1.472111 2.167111 0.3763489 2.400627 0 9.997455 8.835165 9.182993 9.4483 9.672777 9.870519 10.04977 10.22981 10.41738 10.61178 10.81652 11.0309 11.25761 11.49979 11.75945 12.0414 12.35311 12.70798 13.12804 13.67712 Bidder 2 / Valuation 10 Bidders!B10 8.05135 14.91724 11.00001 1.472085 2.167034 0.3763758 2.400414 0 10.03262 8.835478 9.182343 9.449062 9.67268 9.87077 10.04989 10.22986 10.41729 10.61214 10.81625 11.03075 11.25787 11.4997 11.75869 12.04115 12.35408 12.7079 13.12795 13.67451 Bidder 3 / Valuation 10 Bidders!B11 8.045521 14.96837 11 1.472135 2.167182 0.3764645 2.400879 0 10.06799 8.835341 9.182631 9.448283 9.673059 9.870663 10.05006 10.22984 10.41687 10.61192 10.81664 11.03055 11.25828 11.49992 11.75952 12.04112 12.35346 12.70818 13.12862 13.67526 Bidder 4 / Valuation 10 Bidders!B12 8.025686 14.93237 10.99999 1.472066 2.166977 0.3763252 2.40031 0 9.997574 8.835665 9.182904 9.448843 9.672935 9.87027 10.04983 10.22976 10.41727 10.61236 10.81642 11.03119 11.25812 11.49958 11.7591 12.04095 12.35377 12.70773 13.1291 13.67584 Bidder 5 / Valuation 10 Bidders!B13 8.04605 14.93805 11.00002 1.472099 2.167075 0.3763904 2.400517 0 10.03264 8.836273 9.182502 9.448417 9.672706 9.870299 10.04992 10.22979 10.41722 10.61185 10.81611 11.03118 11.2578 11.49951 11.75866 12.04144 12.35373 12.70848 13.12733 13.67634 Bidder 6 / Valuation 10 Bidders!B18 8.025506 14.92361 11 1.472126 2.167155 0.3763362 2.40069 0 9.997495 8.836495 9.182376 9.448744 9.672959 9.870468 10.05011 10.22995 10.41691 10.61189 10.81627 11.03076 11.25787 11.49937 11.75875 12.0408 12.35366 12.70805 13.12768 13.67609 Bidder 7 / Valuation 10 Bidders!B19 8.033243 14.92383 10.99999 1.472068 2.166984 0.3762727 2.400282 0 9.997473 8.836599 9.182738 9.448437 9.67262 9.870665 10.04964 10.23008 10.41675 10.61186 10.81597 11.03117 11.25833 11.49915 11.75933 12.04149 12.35386 12.70753 13.12809 13.67456 Bidder 8 / Valuation 10 Bidders!B20 8.043204 14.94815 10.99999 1.472097 2.16707 0.3763364 2.40054 0 10.06794 8.835606 9.182376 9.449032 9.672697 9.870634 10.05005 10.22963 10.41734 10.61186 10.81668 11.03089 11.25768 11.4993 11.75942 12.04121 12.35314 12.7079 13.12749 13.67509 Bidder 9 / Valuation 10 Bidders!B21 8.026911 14.92783 10.99999 1.472093 2.167059 0.3762503 2.40046 0 10.0326 8.835439 9.182981 9.448875 9.67265 9.870294 10.04989 10.2303 10.41737 10.6125 10.81587 11.03093 11.25816 11.49946 11.75892 12.0418 12.35314 12.70796 13.12912 13.67546 Bidder 10 / Valuation 10 Bidders!B22 8.036841 14.91919 11.00001 1.47214 2.167197 0.3764372 2.400772 0 9.997502 8.835675 9.182334 9.448555 9.673242 9.870429 10.05015 10.2303 10.41722 10.61242 10.81619 11.03076 11.25777 11.49955 11.75932 12.04154 12.35375 12.70723 13.12865 13.67517 RiskTriang($B$4,$B$5,$B$6) RiskTriang($B$4,$B$5,$B$6) RiskTriang($B$4,$B$5,$B$6) RiskTriang($B$4,$B$5,$B$6) RiskTriang($B$4,$B$5,$B$6) RiskTriang($B$4,$B$5,$B$6) RiskTriang($B$4,$B$5,$B$6) RiskTriang($B$4,$B$5,$B$6) RiskTriang($B$4,$B$5,$B$6) RiskTriang($B$4,$B$5,$B$6) RiskTriang($B$4,$B$5,$B$6) RiskTriang($B$4,$B$5,$B$6) RiskTriang($B$4,$B$5,$B$6) RiskTriang($B$4,$B$5,$B$6) RiskTriang($B$4,$B$5,$B$6) a. The 2.436988 expected 0 (mean) 4.862916 price they 0 0 can expect2.400394 is around 0 8.83534 2.400472 $9.615M 0 9.997457 8.83612 9.909346 10.03265 b. The probability of getting0 more than $10M is around 34%. 8.27237 Part 10% Perc 20% Perc 25% Perc 30% Perc 35% Perc 40% Perc 45% Perc 50% Perc 55% Perc 60% Perc 65% Perc 70% Perc 75% Perc 80% Perc 85% Perc 90% Perc 95% Perc c. The extra value of adding0 5 bidders is around $0.432M. This is9.182568 the maximum the 9.182837 8.554775 9.182156 partners should pay. 15% Perc 8.748488 0 9.449081 9.448802 9.448807 8.918979 9.052208 9.204329 9.329852 9.441962 9.54655 9.658016 9.766958 9.879407 9.984748 10.09166 10.20502 10.32541 10.45847 10.61327 10.80074 0 0 0 0 0 0 0 0.1359848 0.278876 0.4262661 0.5787951 0.7515393 0.9168133 1.135605 1.398839 1.771755 9.672786 9.87041 10.04974 10.22999 10.4168 10.61204 10.8165 11.03112 11.25809 11.49938 11.75915 12.04189 12.35423 12.70825 13.12792 13.67647 9.672879 9.870585 10.04956 10.22996 10.41697 10.6122 10.81655 11.03053 11.25832 11.49994 11.75881 12.04177 12.35303 12.70732 13.12889 13.67486 9.672674 9.870166 10.0501 10.2301 10.41668 10.61217 10.81599 11.03091 11.25772 11.49955 11.75887 12.041 12.35413 12.708 13.12796 13.67574 Filter Minimum Filter Maximum Filter Type # Values Filtered Target #1 (Value) Target #1 (Perc%) Target #2 (Value) Target #2 (Perc%) Target #3 (Value) Target #3 (Perc%) Target #4 (Value) Target #4 (Perc%) Target #5 (Value) Target #5 (Perc%) Target #6 (Value) Target #6 (Perc%) Target #7 (Value) Target #7 (Perc%) Target #8 (Value) Target #8 (Perc%) Target #9 (Value) Target #9 (Perc%) Target #10 (Value) Target #10 (Perc%) 0 10 0.6568 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
View Full Document

Ask a homework question - tutors are online