Consider the following linear programming problem Max z = 3A + 2B 3A + 1 B 24 A,

Question

Consider the following linear programming problem Max z = 3A + 2B 3A + 1 B 24 A,B >-0 Suppose that the computer printout give you the following information related to the dual price Constraint RHS Value Allowable Increase 1.2 Allowable Decrease 2 10 24 16 2 6 3 Infinite 3 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

Explanation / Answer

Dual price for constraint 1 = 1.5

z = 27

current RHS of constraint 1 = 10

If RHS is increased by 1, it impacts the z value as per the dual price. the dual states that with each increment of RHS of a constraint the profit or the objective function will improve by the magnitude of dual price.

Hence, new z = 27 + 1*1.5 = 28.5

similarly if the RHS decresed by 2 units. It is allowed since allowable decrease of constraint 1 is 2 units.

the z would decrease by the corresponding dual value.

new z for decrease = 27 - 2*1.5 = 24

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