Question: 2. (20 points) Consider the following L.P. problem, P2 : max C1X1 + C2X2 + c33 + c4X4 s.t. a11X1 + 212X2+ a13X3 + 214X4

2. (20 points) Consider the following L.P.

2. (20 points) Consider the following L.P. problem, P2 : max C1X1 + C2X2 + c33 + c4X4 s.t. a11X1 + 212X2+ a13X3 + 214X4 s bi a21X1 + a22X2 + a23X3 + a24X4 s b2 a31X1 + a32X2 + a33x3 + 234X4 s b3 X1, X2, X3, X4 20 Below is an optimal simplex tableau of P2. Treat the following questions independently. X1 X2 X3 si S2 S3 30 0 20 0 15 0 40 7050 1/3 1 1/3 0 1/2 0 -1/3 35 -1/3 0 -4/3 0 1 1 -5/3 0 1/3 0 4/3 1 -1/2 0 2/3 5 X4 a) What are the original values of the three resources bi, b2, b3? b) What are the current shadow prices of the three resources? For what range of values of b are these shadow prices in effect? c) Can you find another set of shadow prices for these resources (Hint: another dual optimal solution)

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