Consider the linear program given below (almost the same as the previous problem - the only...

Consider the linear program given below (almost the same as the previous problem - the only difference is that the right hand side of the first constraint has been increased from 10 to 11):

Decision variables: A, B, C, and D

Objective: maximize 3 A + 5 B + C +2 D

Constraints:

A + B + C + D <= 11

A – B = 0

A + B – C – D <= 0

Solve it using Excel. How much has the objective function value increased (compared with the earlier case when the right hand side of the first constraint was 10)? (Note: what is needed is the "increase" in objective function value, NOT the new value of the objective function. As before, please assume that all variables are non-negative)

Expert Solution

The increase in the objective function value is "3" (i.e. three).

Explanation: When the cosntraint was 10 it the value of objective function was 30 and when the constraint became 11 then the value of objective function increased to 33. Thus increase = 33 - 30 = 3.

From excel's sensitivity report we can see that the constraint's larange multiplier is 3 and hence when it is increased by 1 (11-10 = 1) then increase in objective function = 1*3 = 3

jeff jeffy answered 1 year ago

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