Find the computer solution, including the ranging (sensitivity analysis) results, for Question 1 by using QM for Windows or Excel. Determine the optimal solution (including the decision variables and the slack/surplus variables) and optimal profit. Interpret the optimal solution and optimal profit:

HERE IS QUESTION 1:

An air conditioning company manufactures three home air conditioners: model A, model A+ and model A++. The profits per unit are $70, $100, and $145, respectively. The production requirements per unit and the availability of the three resources are given below:

	Model A	Model A+	Model A++	Available
Number of fans	1	1	1	400
Number of cooling coils	2	2	4	600
Manufacturing Time	12	16	20	4500 hours

How many model A, model A+ and model A++ air conditioners should the company manufacture in order to maximize profit?

Formulate a linear programming model for the above situation by determining

(a) The decision variables.

(b) Determine the objective function. What does it represent?

(c) Determine all the constraints. Briefly describe what each constraint represents.

HERE ARE THE RESULTS:

Let the number of Model A be x1

Let the number of Model A+ be x2

Let the number of Model A++ be x3

Constraints

x1 + x2 + x3 <= 400 (Number of Fans)

2x1 + 2x2 + 4x2 <= 600 (Number of cooling coils)

12x1 + 16x2 + 20x3 <= 4500 (Amount of manufacturing time)

Objective Function:

Profit Z = 70x1 + 100x2 + 145x3

(a) The decision variables are the suitable values of x1,x2 and x3 for which all the constriants are met and the profit function function Z is maximized

(b) The objective function Z = 70x1 + 100x2 + 145x3 represents the amount of profit that will be going to generate after selling x1 units of A, x2 units of A+ and x3 units of A++

(c) The constraints are given below

x1 + x2 + x3 <= 400 (Number of Fans)

2x1 + 2x2 + 4x2 <= 600 (Number of cooling coils)

12x1 + 16x2 + 20x3 <= 4500 (Amount of manufacturing time)