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.

Let E = number of economy tires manufactured

      P = number of premium tires manufactured

1. What is the maximum allowable decrease in the profit for economy tires, before the optimal decision changes, rounded to the closest whole number?

2. What is the shadow price for final inspection, rounded to the closest whole number?

Answer 1

Let Z be the total profit

Objective function:

Maximize Z = 12E + 10P

Constraints:

(4/3)E + (1/2)P ≤ 600

(4/5)E + P ≤ 650

(1/2)E + (2/4)P ≤ 580

(1/5)E + (1/3)P ≤ 120

ANSWERS:

(1) $6

(2) $21