Formulate but do not solve the following exercise as a linear programming proble

Question

Formulate but do not solve the following exercise as a linear programming problem.

A company manufactures x units of product A, y units of product B, and z units of product C. Each product is processed in three departments: I, II, and III. The total available labor-hours per week for departments I, II, and III is 870, 1790, and 820, respectively. The time requirements (in hours per unit) and profit per unit for each product are given in the table below. How many units of each product should the company produce in order to maximize its profit, P?

Product A Product B Product C Dept. I 2 1 2 Dept. II 3 1 2 Dept. III 2 2 1 Profit $20 $11 $15

Explanation / Answer

Solution:

A company manufactures x units of product A, y units of product B, and z units of product C.

therefore we have to maximize obejctive function

p = 20x + 11y + 15z

subjected to the Constraints

department 1

2x + y +2z 870

Department

3x +y + 2y 1790

Department 3

2x +2y +z 820

x 0 y 0 z 0

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