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IOE 310 - Additional Problems B For additional practice only. Not collected. Problem 1 Consider the following LP: max z = 5 x 1 + 3 x 2 + x 3 s.t 2 x 1 + x 2 + x 3 6 x 1 + 2 x 2 + x 3 7 x 1 , x 2 , x 3 0 (a) Graphically solve this problem. (b) Use complementary slackness to solve the max problem.

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IOE 310 – Additional Problems B Page 2 of 9 Problem 2 Consider the following LP and its optimal tableau: max z = 5 x 1 + x 2 + 2 x 3 s.t x 1 + x 2 + x 3 6 6 x 1 + + x 3 8 x 2 + x 3 2 x 1 , x 2 , x 3 0 z x 1 x 2 x 3 s 1 s 2 s 3 rhs 1 0 1/6 0 0 5/6 7/6 9 0 0 1/6 0 1 -1/6 -5/6 3 0 1 -1/6 0 0 1/6 -1/6 1 0 0 1 1 0 0 1 2 (a) Find the dual to this LP and the optimal solution to the dual. (b) Find the range of values of c 2 for which the current basis remains optimal. This additional problem set was developed for IOE 310, fall semester 2010. This document may not be copied or distributed.
IOE 310 – Additional Problems B Page 3 of 9 Problem 3 Consider the following LP and its optimal tableau: max z = 3 x 1 + x 2 x 3 s.t 2 x 1 + x 2 + x 3 8 4 x 1 + x 2 x 3 10 x 1 , x 2 , x 3 0 z x 1 x 2 x 3 s 1 s 2 rhs 1 0 0 1 1/2 1/2 9 0 0 1 3 2 -1 6 0 1 0 -1 -1/2 1/2 1 (a) Find the dual to this LP and the optimal solution to the dual. (b) Find the range of values of b 2 for which the current basis remains optimal. If b 2 = 12, what is the new optimal solution? This additional problem set was developed for IOE 310, fall semester 2010. This document may not be copied or distributed.

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IOE 310 – Additional Problems B Page 4 of 9 Problem 4 Use the Theorem of Complementary Slackness to find the optimal solution to the following LP and its dual: max z = 3 x 1 + 4 x 2 + x 3 + 5 x 4 s.t x 1 + 2 x 2 + x 3 + 2 x 4 5 2 x 1 + 3 x 2 + x 3 + 3 x 4 8 x 1 , x 2 , x 3 , x 4 0 Problem 5
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