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 Manufacturing Time Coils (hours ) Economy 8 Standard 12 Deluxe 14 For the coming production period , the company has 200 fan motors , 320 cooling coils , and 2400 hours of manufacturing time available . How many economy models (E), standard models (S), and deluxe model (D) should the company produce in order to maximize profit ? The linear programming model for the problem is as follows . Max 63E 95S 135D S.L . IE S 200 Fan motors 4D 320 Cooling coils BE 125 14D 2400 Manufacturing time E,S,D 20 Sensitivity Report Variable Final Value Reduce Objective Allowable Allowable Cost Coefficient Increase Decrease E Economy Models 80.000 0.000 63.000 2.000 15.500 Standard Models 120.000 0.000 95.000 31.000 8.000 D Deluxe Model 0.000 -24.000 135.000 24.000 IE + 30 Constraint Final Value Shadow Right Hand Allowable Allowable Price Side Increase Decrease 1 Fan Motors 200.000 31.000 200.000 80.000 40.000 Cooling Coils 320.000 32.000 320.000 80.000 120.000 Manufacturing Time 2080.000 0.000 2400.000 LE +30 320.000 "What is the optimal solution and what is the value of the objective function Which constraints are binding ? Which constraint shows extra capacity and how much ? 3. If the profit for the deluxe model were increased to $150 per unit , would the optimal solution change ? 4. What is the range of optimality for each objective function coefficient ? 5. 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 deluxe model is increased by $4 per unit . What will the new objective function value be? 6. Identify the range of feasibility for the right -hand -side values . 7. If the number of fan motors available for production is increased by 100 , will the shadow price for that constraint change ? Why