Answer Happy

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 220 fan motors, 340 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: (a) Use Linear Programming Excel Solver Solution to Determine the optimal mix of air conditioners to produce to to maximize the profit. In other words, how many of each of the three air conditioners should the manufacturer produce? (b) Based on the results in part (a), identify and interpret the range of optimality for each of the three objective function coefficients. {Interpretation Hint: The solution of [x₁ =12 rolltop desks] and [x₂ = 4 regular desks] remains optimal as long as the [profit per unit of a rolltop desk] remains between [$45] and [$135]} (c) What is the estimated change in the objective function value (i.e., profit) if the company were to obtain 50 additional fan motors? {Interpretation Hint: An increase of one unit in the right-hand-side value of the [Maple Constraint] leads to a change of [7 dollars] in [total profit of Sidneyville]}