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Question: Partial of the Excel Solver Sensitivity Report for the LP model in Problem (3) is provided b...

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Partial of the Excel Solver Sensitivity Report for the LP model in Problem (3) is provided below.

Microsoft Excel 16.0 Sensitivity Report
Variable Cells
		Final	Reduced	Objective	Allowable	Allowable
Cell	Name	Value	Cost	Coefficient	Increase	Decrease
$G$5	Units LaserStop	0	-80	124	80	1E+30
$H$5	Units SpeedBuster	333	0	136	1E+30	53.3

(a) If the unit profit for LaserStop changes from $124 to $210, will the optimal solution and total profit change? Explain.

(b) If the unit profit for SpeedBuster changes from $136 to $100, will the optimal solution and total profit change? Explain.

Answer 1

The allowable increase/decrease associated with the original coefficient of a decision variable tells us the range in which the coefficient of a given decision variable in the objective function may be increased/decreased without changing the optimal solution.

(a)

If LaserStop changes from $124 to $210, the increase in the coeffcient is 210 - 124 = 86. Since the increase of 86 is less than the allowable increase of 80, the optimal solution would not change. Also, the final value for LaserStop is 0, so the total profit would not change.

(b)

If SpeedBuster changes from $136 to $1000, the decrease in the coeffcient is 136 - 100 = 36. Since the decrease of 36 is less than the allowable decrease of 53.3, the optimal solution would not change. The final value for SpeedBuster is 333, so the total profit decrease by 333 * 36 = 11988.