linear programming

18. Quality Air Conditioning manufactures three home air conditiOners: an economy model, a standard model, and a deluxe mode}. The profits per unit are $63, $95, and $135, rcspec_ tively. The production requirements per unit are as follows: Number of Number of Manufacturing Fans Cooling Coils Time (hours) Economy 1 1 8 Standard 1 2 12 Deluxe 1 4 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 models (D) should the company produce in order to maximize prot? The linear programming model for the problem is as follows: Max 635 + 955 + 135D S.t. 1E + IS + 1D 5 200 Fan motors 18+ 25 + 41) 5 320 Cooling coils SE 4- 12S + 14D 5 2400 Manufacturing time E&020 The computer solution using The Management Scientist is shown in Figure 3.17. a. What is the Optimal solution, and what is the value of the objective function? 1). Which constraints are binding? c. Which constraint shows extra capacity? How much? (i. If the prot for the deluxe model were increased to $150 per unit, would the optimal solution change? Use the information in Figure 3.17 to answer this question. 1?. Refer to the computer solution of Problem 18 in Figure 3.17. a. b0 Identify the range of optimality for each objective function coefcient. Suppose the prot for the economy model is increased by $6 per unit, the prot for the standard model is decreased by $2 per unit, and the prot for the deluxe model is increased by $4 per unit. What will the new optimal solution be? Identify the range of feasibility for the righhandside values. If the number of fan motors available for production is increased by 100, will the dual price for that constraint change? Explain. FIGURE 3.1? THE MANAGEMENT SCIENTIST SOLUTION FOR THE QUALITYAIR CONDITIONING PROBLEM H Objective Function Value = 16440.000 Variable Value Reduced Costs E 80.000 0.000 S 120.000 0.000 D 0.000 24.000 Constraint Slack/Surplus Dual Prices 1 0.000 31 000 2 0.000 32.000 3 320.000 0.000 'Variable Lower Limit Current value upper Limit E 47.500 63.000 75 000 a 87.000 95.000 126 000 D No Lower Limit 135.000 159.000 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit 1 160.000 200.000 200.000 2 200.000 320.000 400.000 3 2000.000 _ 2400.000 Nb Upper Limit M