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Unformatted text preview: Test 4 NameLM
Math 2602 5_ April '21, 2005 <3 #5 eqoln) (1) (9 points) The following matrices are in the form [AW]. For
each 'of them, say how many solutions there are to the equa  tion A5 = Ethere are and give a brief explanation showing
how you know. (a)
63214 431'? summg
0 54 2 3 0‘54? 3 aromaFiat):
4, 00451 A» om 11.: . 0 0 4 5 1 a5 ! u
0 0 DO 0  . .
Tauq I soivh'ons _I
(b)
6 3 21 4 .6 3, 2 I I4 “4453544445
3 (5} i g _32 —> o 5 q 2 . 3 ‘MMSI'skemIs ’
0045 1 ‘ 09'15 —1 Ineaati43+5x=~z
riftq ‘7 o o 0 3 and 4x3+5xq =1.)
so 319 SOluh'ns
(C)
_6_ 3 2 1 4
0:5, 4 2 3 fhunl‘saP‘V°+ih
0 0 _4 5 1 W3 Column .56
U U 0;). 1 M IS Wadi13 9L?
1 $°IU+br\ In: (2) (12 points) Cousin Henry wants to grow potatoes and corn
next season, and he is trying to decide how much of each to
grow. 0" eﬁunl +0 o He wants his total purchases to weigh less/than A1 5 pounds. 0 Each bag of starter potatoes weighs 3 pounds, and each
bag of corn seeds weighs 1 pound. c He has only twenty acres to plant. a Each bag is designed to plant 1 acre.  He can get 10 dollars for each acre of potatoes he plants
and 5 dollars for each acre of corn. Using the variables p and c for the number of bags of potatoes
and corn respectively, a ' (a) Write down the constraint equations which govern this
process: ‘ 3P+1C£ls P+c s 20
P,c>,o (b) Draw the feasible solution space, labeiing all vertices with
their‘foordinates: ‘ .m» \l (5 pk) son‘3 H’ '15
We. mos!" ﬁlmsHy 55 l Vt't'o‘n 593% CAAQMELd one 0+ " 'l'ic. mumbe/stb +14; Midﬁrm easier '
to read. 4 ich. n
COIS SOIUha Gnﬁ W Soyvhnoln Space (c) Write the simplex tableau Cousin Henry would use to ign‘f Mfg H}.
maximize his profit: “‘5 . C3 Fir. act)
(3) (9 points) Here are some constraint equations:
$+y+321
23: + 5y + 32 g 6
:23, 31,2 2 0 (a) Explain why using the twophase method simplex algo—
rithm is a good way to proceed: EH‘ner
0 Ort‘jin is nol— in SolUl't'bln spam
° ‘Henc is no slat—[c VG/Vt'cblabu b.3555 (b) Rewrite the equations adding the appropriate variables ixrvlq—Z—Sl +l3l== ‘ éslquUMfQJaLeiS I. ‘ W0 Wt. ."I" Zx+53+32 i5; ‘l'Bleﬁ Naoth M) XIV) 2.: Sr .381, BUB; 7/0
‘ (c) Give the starting tableau for phase l. .  ' c, . 
('4) (3 points) Given the following tableau; what hapﬂEpens ngxt in I the simplex method, and what does that tell you? flue“. [.5 a. Column WM ‘I'Le. Dal) psifive.
ﬁm+bij “\Oh}E#m+WA rmﬁ $0 m30f1+hm 6+°P5 M SOIthn space “IS 100 . _
dirtdion Un undedm +L‘9X3 (5) (12 points.) Given the toliowing simplex tableau: W
S Crﬂ'i’ohucoricll Mug? 05% as Pivci'l' since. X; is (>an ' 0 0 ~29; o ’2 —g C) —2 Z '48
column w/pasilwbvalvﬁa 1 Q D 0 G. i 3 1 Z
in obj. ¥0no+tbn mo 0 0 4 0 —2 —1 z—mlOO mi ' L _ e 6 '3'
“a V3 3 ‘ m/ (a) 80mplete the optimization using the simpiex method ow... «r o a. l
/3rI '1: o o q 0 ~14 a“
l——_——————————I—'_‘—I_.___—_
*Zr +r a ‘ ' 4‘ o
I 2 “O O [3 22h;
F.+r3
J; 
0 4/3 0 o 4 ‘73 2—"; ‘Lygrl'i'r‘l '  ‘
gina.‘ +m‘sicau (itemi b) HﬁQ (b) Give the coordinates of the optima! basic feasibie solu—
tion, and give the final value for the maximum of the ob
jective function. x1 X3 ‘3! M Piuoi V‘Lriwbhs co alga. tIS ﬁve '50 XI gig is Soluh'bn
X5 = 3 (1530,316Ao)
5,— 6 and dDJ‘FunC/hbn maximized 0+ WUUC ...
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 Math, Optimization, Emoticon, ASCII art, Constraint, simplex tableau, simplex tableau Cousin

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