Question

Gatson manufacturing company produces 2 types of tires: Economy tire; Premium tire. The manufacturing time and the profit contribution per tire are given in the following table.

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​ Operation	Manufacturing Time (Hours)	Time Available
	Economy tires	Premium tires	Hours
Material Preparation	4/3	1/2	600
Tire Building	4/5	1	650
Curing	1/2	2/4	580
Final Inspection	1/5	1/3	120
Profit/Tire	$12	$10

Answer the following assuming that the company is interested in maximizing the total profit contribution.

a. Develop a spreadsheet model and find the optimal solution using Excel Solver. What is the total profit contribution Gatson can earn with the optimal production quantities? Enter your answer without a dollar sign and rounded to two decimal places.

b. Based on your answer to Question 1, how many Economy tires should Gatson manufacture to maximize profit contribution? Round your answer to one decimal place.

c. Based on your answer to Question 1, how many Premium tires should Gatson manufacture to maximize profit contribution? Round your answer to one decimal place.

Answer 1

a.

Let,

E = number of economy tires to produce
P = number of premium tires to produce

objective is to maximize profit = Max 12E+10P

subject to,

4E/3+P/2 <= 600
or, 8E+3P <= 3600 (Material preparation)

4E/5+P <= 650

or, 4E+5P <= 3250 (Tire building)

E/2+2P/4 <= 580
or, 2E+2P <= 2320 (Curing)

E/5+P/3 <= 120 (Final inspection)
or, 3E+5P <= 1800

E,P >= 0

Solving in solver we get,

Total maximized profit contribution = 6038.709677 = 6038.71 (Rounded to 2 decimal places)

Solver screenshot

Solver formula

Solver window

b.

number of economy tires to produce to maximize profit contribution = 406.4516129 = 406.45(Rounded to 2 decimal places)

c.

number of premium tires to produce to maximize profit contribution = 116.1290323 = 116.13 (Rounded to 2 decimal places)