Question

Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $67, $93, and $129, respectively. The production requirements per unit are as follows: Number of Manufacturing Number of Cooling Coils Time (hours) Fans Economy Standard 12 Deluxe 14 For the coming production period, the company has 250 fan motors, 360 cooling coils, and 1800 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 Max 67E93S129D s.t. 1E+1S1D 250 Fan motors 1E24Ds 360 Cooling coils BE12514D s 1800 Manufacturing time The computer solution is shown in the figure below. Optimal Objective Value15780.00000 Variable Reduced Cost Value 120.00000 0.00000 0.00000 60.00000 0.00000

Slack/Surplus Dual Value Constraint 0.00000 5,22222 7.72222 Objective Allowable Allowable Variable Coefficient Increase Decrease 67.00000 6.71429 9,10000 Infinite 93.00000 129.00000 139.00000 11.75000 Allowable RHS Constraint Value Increase Decrease Infinite 250.00000 70.00000 360.00000 154.28570 135.00000 1800.00000 420.00000 540.00000

a. What is the optimal solution, and what is the value of the objective function? If required, round your answers to the nesrest whole number. If your answer is zero, enter "o" Optimal Solution Economy models (E) Standard models (S) Deluxe models (D) Value of the objective function b. Which constraints are binding? Fan motors: Cooling coils Binding Manufacturing time Non binding

c. Which constraint shows extra capacity? How much? If constraint shows no extra capacity, enter 0 as number of units. If required, round your answers to the nearest whole number. Number of units Constraints Extra capacity Fan motors Cooling coils Yes Manufacturing time No

d. If the profit for the standard model were increased to $108 per unit, would the optimal solution change? The optimal solution change because the profit of the standard model can vary from ▼ , $108 is Y this range without the optimal solution to changing

Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $67, $93, and $129, respectively. The production requirements per unit are as follows: Number of Manufacturing Number of Cooling Coils Time (hours) Fans Economy Standard 12 Deluxe 14 For the coming production period, the company has 250 fan motors, 360 cooling coils, and 1800 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 Max 67E93S129D s.t. 1E+1S1D 250 Fan motors 1E24Ds 360 Cooling coils BE12514D s 1800 Manufacturing time The computer solution is shown in the figure below. Optimal Objective Value15780.00000 Variable Reduced Cost Value 120.00000 0.00000 0.00000 60.00000 0.00000 Slack/Surplus Dual Value Constraint 0.00000 5,22222 7.72222 Objective Allowable Allowable Variable Coefficient Increase Decrease 67.00000 6.71429 9,10000 Infinite 93.00000 129.00000 139.00000 11.75000 Allowable RHS Constraint Value Increase Decrease Infinite 250.00000 70.00000 360.00000 154.28570 135.00000 1800.00000 420.00000 540.00000 a. What is the optimal solution, and what is the value of the objective function? If required, round your answers to the nesrest whole number. If your answer is zero, enter "o" Optimal Solution Economy models (E) Standard models (S) Deluxe models (D) Value of the objective function b. Which constraints are binding? Fan motors: Cooling coils Binding Manufacturing time Non binding c. Which constraint shows extra capacity? How much? If constraint shows no extra capacity, enter 0 as number of units. If required, round your answers to the nearest whole number. Number of units Constraints Extra capacity Fan motors Cooling coils Yes Manufacturing time No d. If the profit for the standard model were increased to $108 per unit, would the optimal solution change? The optimal solution change because the profit of the standard model can vary from ▼ , $108 is Y this range without the optimal solution to changing

Answer 1

Answer :

b)The asset limitations that have slack/surplus esteem equivalent to zero are accepted that be totally fulfilled or consumed.Thus such asset imperatives are authoritative or restricting the optimal solution.

Fan motor	Binding
Cooling coils	Binding
Manufacturing time	Non binding

c)The asset limitations those are authoritative or restricting the optimal solution,there is no additional limit where as the non restricting requirements are not totally used for every imperative these are balance sum remained.

Constraints	Extra capacity	No.of units
Fan motors	No	70
Cooling coils	No	0
Manufacturing time	No	0

d)The stipends increments and diminishing qualities for the choice variable,represents the scope of expense or benefit coefficient will be in optimal solution.For the variable D.Allowable increments when the benefit coefficient of the zero is expanded to $ 93 + 10.11 = $ 103.11,the variable is incorporated ideal arrangement.

The optimal solution won't change in light of the fact that the benefit of the exclusive can shift from $ 0 to $ 103.11.$ 108 is will in this without the optimal solution evolving.