Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profit per unit are $63, $95, and $135, respectively. The production requirements per unit are as follows.

Number Number of Manufacturing of 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, 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 maximise profit? The linear programming model for the problem is as follows:

Max 63E + 95S + 135D

s.t. 1E + 1S + 1D <= 200 Fan motors 1E + 2S + 4D <= 320 Cooling coils 8E + 12S + 14D <= 2400 Manufacturing time

E, S, D >= 0

The Computer Solution Excel Sensitivity Report is shown below in Table 1.

Table 1: Microsoft Excel 16.0 Sensitivity Report

Variable Cells Final Reduced Objective Allowable Allowable Variable Value Cost Coefficient Increase Decrease E 80 0 63 12 15.5 S 120 0 95 31 8 D 0 -24 135 24 1E+30

Constraints Final Shadow Constraint Allowable Allowable Variable Value Price R.H. Side Increase Decrease E 200 31 200 120 40 S 320 32 320 80 120 D 320 0 2400 1E+30 2080

Use the information in Table 1 above answer the following questions from a-g.

(a) What is the optimal solution and what is objective function value? (b) Which Constraints are binding? (c) Which constraints show extra capacity? How much? (d) If the profit for deluxe model were increased to $150 per unit, would the optimal solution change? Explain showing brief calculations. (e) Identify and calculate range of optimality for each objective function coefficient.

(f) Identify the range of feasibility for the right-hand-side values.

(g) If the number of fan motors available for production increased by 100, will the dual value for that constraint change? Explain showing brief calculations.