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Based on the following sensitivity report, what would be the change in the objective function value...

Based on the following sensitivity report, what would be the change in the objective function value if the objective function coefficient for Product_2 increases to 19?

Cell $B$3 Name Product_2    Final Value 175 Reduced Cost 0   Objective Coefficient 14 Allowable Increase 9 Allowable Decrease 1

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Answer #1

The final value of the variable Product_2 = 175

The current objective coefficient of variable Product_2 = 14

The allowable increase of the coefficient = 9

The allowable decrease of the coefficient = 1

If the objective function coefficient for Product_2 increases to 19 from 14, it will be within the allowable increase of the objective function coefficient. Hence the optimal solution will remain the same. The optimal value of the Product_2 variable will thus be 175.

The objective function value will increase by a value = 175 * 19 - 175 * 14

= 175 * (19 - 14)

= 175 * 5

= 875

Thus the objective function value will increase by 875.

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