Formulate but do not solve the following exercise as a linear programming problem. A company manufactures products A, B, and 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 are 970, 1,090, and 860, respectively. The time requirements (in hours per unit) and profit per unit for each product are as follows: How many units of each product should the company produce in order to maximize its profit?
A) Maximize: Subject to:
B) Maximize: Subject to:
C) Maximize: Subject to:
D) Maximize: Subject to:

Question

Formulate but do not solve the following exercise as a linear programming problem. A company manufactures products A, B, and 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 are 970, 1,090, and 860, respectively. The time requirements (in hours per unit) and profit per unit for each product are as follows:  How many units of each product should the company produce in order to maximize its profit?
A) Maximize: Subject to: 
B) Maximize: Subject to: 
C) Maximize: Subject to: 
D) Maximize: Subject to:

Quizplus · Accepted Answer

The objective is to maximize profit, which is given in the table as the profit per unit for each product. The decision variables are the number of units of each product to produce. The constraints are the available labor-hours in each department, which are given in the problem. Therefore, the correct formulation is:

Maximize: 
Profit A + Profit B + Profit C

Subject to: 
Labor-hours required for A in department I + Labor-hours required for B in department I + Labor-hours required for C in department I <= 970 
Labor-hours required for A in department II + Labor-hours required for B in department II + Labor-hours required for C in department II <= 1090 
Labor-hours required for A in department III + Labor-hours required for B in department III + Labor-hours required for C in department III <= 860

Where Profit A, Profit B, and Profit C represent the profit per unit for each product.

Formulate but Do Not Solve the Following Exercise as a Linear