Consider the following linear programming pr Max z 3A + 2B oblem 1A 1B10 3A+1B(2

Question

Consider the following linear programming pr Max z 3A + 2B oblem 1A 1B10 3A+1B(224 1A + 2B 0 Suppose that the computer printout give you the following information related to the dual price Constraint RHS Value Allowable Increase Allowable Decrease 10 24 16 Infinite The dual value for constraint 1 is 1.5. Explicitly express how the optimal objective function value of z 27 would change if the right hand side of constraint 1 is increased by 1 unit. Specifically, state the new value of z. Similarly, suppose that the right hand side value of constraint 1 is decreased by 2 units. Specifically, state how the optimal objective function value of z 27 would change if the right hand side of constraint 1 is increased by 1 unit. State the new value of z. Special Note To answer this question you should follow and specific script. First state if the change to the right hand side is within the range. If the change is within the range, what does this mean for the dual price? Specifically, is the current dual price valid or not. If the dual price remains valid, calculate the new z-value with the specified change. If the dual price is not valid, you must resolve the problem.

Explanation / Answer

Answer

given by

Specified that Dual value (shadow price) of limitation 1 is 0.5

Part1: Increase the true hand side of the constriction 1 by 1

As the vary in the right hand side of the limitation 1 is within the permissible limits (8, 11.2) of the constriction 1, the dual price of the limitation 1 is valid within this series.

As the dual fee is valid within this array, the new z-value will amplify by 1 * 0.5 = 0.5.

This resource the new z-value (optimal objective function value) would be one and the same to 27 + 0.5 = 27.5.

New z-value motivation be 27.5.

Part2: cut the right hand side of the restriction 1 by 2

As the adjust in the right hand side of the constriction 1 is within the allowable limits (8, 11.2) of the Constraint 1, the double price of the Constraint 1 is valid in this range.

As the dual price is valid in this range, the new z-value will dwindle by 2 * 0.5 = 1.

This means the new z-value (optimal objective function value) would be alike to 27 – 1 = 26.

New z-value willpower be 26.

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