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 900, 1080, and 840, respectively. The time requirements (in hours per unit) and profit per unit for each product are as follows. (For example, to make 1 unit of product A requires 2 hours of work from Dept. I, 3 hours of work from Dept. II, and 2 hours of work from Dept. III.) Product A Product B Product C Dept. I 2 1 2 Dept. II 3 1 2 Dept. III 2 2 1 Profit $72 $48 $60 How many units of each product should the company produce in order to maximize its profit? What is the largest profit the company can realize? Are there any resources left over?
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 900, 1080, and 840, respectively. The time requirements (in hours per unit) and profit per unit for each product are as follows. (For example, to make 1 unit of product A requires 2 hours of work from Dept. I, 3 hours of work from Dept. II, and 2 hours of work from Dept. III.) Product A Product B Product C Dept. I 2 1 2 Dept. II 3 1 2 Dept. III 2 2 1 Profit $72 $48 $60 How many units of each product should the company produce in order to maximize its profit? What is the largest profit the company can realize? Are there any resources left over?
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.CT: Test
Problem 24CT
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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 900, 1080, and 840, respectively. The time requirements (in hours per unit) and profit per unit for each product are as follows. (For example, to make 1 unit of product A requires 2 hours of work from Dept. I, 3 hours of work from Dept. II, and 2 hours of work from Dept. III.)
| Product A | Product B | Product C | |
|---|---|---|---|
| Dept. I | 2 | 1 | 2 |
| Dept. II | 3 | 1 | 2 |
| Dept. III | 2 | 2 | 1 |
| Profit | $72 | $48 | $60 |
How many units of each product should the company produce in order to maximize its profit?
What is the largest profit the company can realize?
Are there any resources left over?
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