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 $65, $97, and $139, 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 350 fan motors, 360 cooling coils, and 3000 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 65E + 97S + 139D s.t. 1E + 1S + 1D 350 Fan motors 1E + 2S + 4D 360 Cooling coils 8E + 12S + 14D 3000 Manufacturing time E, S, D 0 The computer solution is shown in the figure below. Optimal Objective Value = 23070.00000 Variable Value Reduced Cost E 340.00000 0.00000 S 10.00000 0.00000 D 0.00000 22.00000 Constraint Slack/Surplus Dual Value 1 0.00000 33.00000 2 0.00000 32.00000 3 160.00000 0.00000 Variable Objective Coefficient Allowable Increase Allowable Decrease E 65.00000 11.00000 16.50000 S 97.00000 33.00000 7.33333 D 139.00000 22.00000 Infinite Constraint RHS Value Allowable Increase Allowable Decrease 1 350.00000 10.00000 170.00000 2 360.00000 40.00000 10.00000 3 3000.00000 Infinite 160.00000 What is the optimal solution, and what is the value of the objective function? If required, round your answers to the nearest whole number. If your answer is zero, enter "0". Optimal Solution Economy models (E) Standard models (S) Deluxe models (D) Value of the objective function $ Which constraints are binding? Fan motors: Cooling coils: Manufacturing time: 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. Constraints Extra capacity Number of units Fan motors Cooling coils Manufacturing time If the profit for the deluxe model were increased to $154 per unit, would the optimal solution change? The optimal solution change because the profit of the deluxe model can vary from to . $154 is this range without the optimal solution changing.