Module 2: LP Sensitivity Analysis (QUESTION 1)

1. DETAILS ASWMSCI 15 3.E.013. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respectively. The production requirements per unit are as follows: Number of Fans Number of Cooling Coils Manufacturing Time (hours) Economy 1 1 8 Standard 1 2 12 Deluxe 1 4 14 For the coming production period, the company has 240 fan motors, 360 cooling coils, and 2,500 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows: 63E + 95S + 135D Max s.t. 1E + 15 + 1E + 25 + 8E + 12S + 1D S 240 4D S 360 14D S 2,500 E,S,D Fan motors Cooling coils Manufacturing time The computer solution is shown below. Optimal Objective Value = 18960.00000 Variable E Value 120.00000 120.00000 0.00000 Reduced Cost 0.00000 0.00000 24.00000 S D Constraint 1 Slack/Surplus 0.00000 0.00000 100.00000 Dual Value 31.00000 32.00000 0.00000 2 3 Variable E Objective Coefficient 63.00000 95.00000 135.00000 Allowable Increase 12.00000 31.00000 24.00000 Allowable Decrease 15.50000 8.00000 Infinite S D Constraint RHS Value Allowable Increase Allowable Decrease Constraint RHS Value 240.00000 360.00000 2500.00000 Allowable Increase 25.00000 25.00000 Infinite Allowable Decrease 60.00000 120.00000 100.00000 3 (a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) E to S to D to (b) Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal solution be? E units S units D units profit $ (c) Identify the range of feasibility for the right-hand-side values. (If there is no upper or lower limit, enter NO LIMIT.) constraint 1 to constraint 2 to constraint 3 to (d) If the number of fan motors available for production is increased by 45, will the dual value for that constraint change? Explain. Yes, the dual value will change because 45 is greater than the allowable increase of 12. Yes, the dual value will change because 45 is greater than the allowable increase of 25. O No, the dual value will not change because 45 is less than the allowable increase of 265. No, the dual value will not change because there is no upper limit to how much the constraint can increase