Question

An air conditioning company manufactures three home air conditioners: a regular model, a super model, and a deluxe model. The profits per unit are $50, $70, and $140, respectively. The production requirements per unit and the availability of the three resources are given below:

	Regular Model	Super Model	Deluxe Model	Available
Number of fans	1	1	1	420
Number of cooling coils	1	2	4	650
Manufacturing Time	10	15	20	4500 hours

How many regular models, super models, and deluxe models should the company manufacture in order to maximize profit?

(a) Formulate a linear optimization model for this problem.

(b) Solve this model by using the Excel Solver. Include Excel output with you answer as screenshot.

(c) Determine the optimal solution. Interpret and make recommendations based on the optimal solution.

Answer 1

Answer:-

Given That:-

An air conditioning company manufactures three home air conditioners: a regular model, a super model, and a deluxe model. The profits per unit are $50, $70, and $140, respectively.

(a) Formulate a linear optimization model for this problem.

Max Z = 50x1 + 70x2 + 140x3

S.t.

x1 + x2 + x3 420

x1 + 2x2 + 4x3 650

10x1 + 15x2 + 20x3 4500

and x1,x2,x3 0

(b) Solve this model by using the Excel Solver. Include Excel output with you answer as screenshot.

Formulae:

Solver Parameters:

(c) Determine the optimal solution. Interpret and make recommendations based on the optimal solution.

Excel Solution:

The solution indicates that the company should make 250 units of x1 and 100 units of x2 and no units of x3 to maximise the profit. The constraint 2 and 3 are binding constraints while constraint 1 is not binding.

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