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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. Manufacturing Time Hours) Time Available Operation aterial Preparation Tire Building Curing Final Inspection rofit Tire Economy tiresPremium tires Hours 600 650 580 120 4/3 1/2 1/2 1/5 $12 2/4 1/3 $10 Answer the following assuming that the company is interested in maximizing the total profit contribution.
a. What is the linear programming model for this probiem?
b. How many tires of each model should Gatson manufacture?
c. What is the total profit contribution Gatson can earn with the optimal production quantities?

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Answer:

(a)Let X1 be the number of economy tires and X2 be the number of premium tires.

Objective function:

Maximize Z, where Z = 12X1 + 10X2

Subject to constraints

4X1/3 + X2/2 <= 600

4X1/5 + X2 <= 650

X1/2 + 2X/4 <= 580

X1/5 + X2/3 <= 120

X1, X2 = Z

(b) Check attachment for spreadsheet

(c) The maximum profit that can be obtained is $6032

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