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  3. 1. [25 marks] consider the following model: maximi

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

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Advance Math

1. [25 marks] Consider the following model: maximize 40x1 +50x2subject to: x1 +2x2 ? 40 4x1 +3x2 ? 120 x1, x2 ? 0 The optimalsolution, 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 currentsolution 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 interms of ?b, and hence determine its shadow price.

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