Consider the following model: maximize 40x1 +50x2 subject to: x1 +2x2 ≤ 40 4x1 +3x2 ≤...

Consider the following model: maximize 40x1 +50x2 subject to: x1 +2x2 ≤ 40 4x1 +3x2 ≤ 120 x1, x2 ≥ 0 The optimal solution, determined by the two binding constraints, is x1 = 24, x2 = 8, OFV∗ = 1,360. Now consider a more general objective function, c1x1 + c2x2. Perform a sensitivity analysis to determine when the current solution remains optimal in the following cases: (i) both c1 and c2 may vary; (ii) c2 = 50, c1 may vary; (iii) c1 = 40, c2 may vary. Suppose the RHS of the second constraint increases by an amount ∆b. (It is now 120 + ∆b.) Solve the two equations for x1 and x2 in terms of ∆b, and hence determine its shadow price.

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Colby Messinger answered 2 years ago

1. [25 marks] Consider the following model: maximize 40x1 +50x2 subject to: x1 +2x2 ≤ 40...

1. [25 marks] Consider the following model: maximize 40x1 +50x2 subject to: x1 +2x2 ≤ 40 4x1 +3x2 ≤ 120 x1, x2 ≥ 0 The optimal solution, determined by the two binding constraints, is x1 = 24, x2 = 8, OFV∗ = 1,360. Now consider a more general objective function, c1x1 + c2x2. Perform a sensitivity analysis to determine when the current solution remains optimal in the following cases: (i) both c1 and c2 may vary; (ii) c2 = 50,...

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