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Test4_solutions

# Test4_solutions - Test 4 NameLM Math 2602 5 April'21...

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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 aroma-Fiat): 4, 00451 A» om 11.: . 0 0 4 5 1 a5- ! u 0 0 DO 0 - . . Tau-q 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's-kem-I-s ’- 0045 1 -‘ 09'15 —1 Ineaati43+5x=~z rift-q ‘7 o o 0 3 and 4x3+5xq =1.) so 319 SOlu-h'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 I-S Wadi-13 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‘fo-ordinates: ‘ .m» \l (5 pk) son-‘3 H’ '15 We. mos!" ﬁlms-Hy 55 l Vt't'o‘n 593% CAAQMELd- one 0+ " 'l'i-c. mumbe/stb +14; Mid-ﬁrm 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 two-phase method simplex algo— rithm is a good way to proceed: EH-‘ner 0 Ort‘jin is no-l— in SolU-l't'bln spam ° ‘H-enc is no slat—[c VG/Vt'cblabu b.3555 (b) Rewrite the equations adding the appropriate variables ix-rvlq—Z—Sl +l3l==| ‘ é-slquUMfQJaLeiS I. ‘ W0 Wt. ."I" Zx+53+32 i5; ‘l'Bl-eﬁ 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) psi-five. ﬁm+bij “\Oh}E#m+WA rmﬁ \$0 m30f1+hm 6+°P5 M SOIthn space “IS 100 . _ dirtdion Un undedm +L‘9-X3 (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/pasi-lwbvalvﬁa 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 22-h; F.+r3 J; - 0 4/3 0 o 4- ‘73 2—"; ‘Lygrl'i'r‘l ' - ‘ gina.‘ +m‘sicau (item-i b) Hﬁ-Q (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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Test4_solutions - Test 4 NameLM Math 2602 5 April'21...

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