A clothing company produces three types of sport jackets (types 1, 2, and 3), each with different resource requirements (hours of labor, units of leather, and units of wool). The unit costs of these resources are $5 per hour of labor, $7 per unit of leather, and $3 per unit of wool. In each production cycle, the company has 1000 hours of labor available, 800 units of leather, and 900 units of wool. To avoid inventory surplus at the end of the production cycle, the sales department has set maximum production limits for each jacket type, stipulating that no more than 200 jackets of type 1, 100 jackets of type 2, and 150 jackets of type 3 should be produced. The company aims to determine the optimal production plan for the next production cycle to maximize total profit, while adhering to the constraints of resource availability and production limits. Type 1 Type 2 Type 3 Labor time required (hours) 3 2 2 Leather (units) 3 2 0.5 Wool (units) 0.5 2 3 Sale price ($/jacket) $50 $38 $29 1. Formulate an optimization model (decision variables, objective function, and constraints) to help the company identify the optimal production plan. 2.
A clothing company produces three types of sport jackets (types 1, 2, and 3), each with different resource requirements (hours of labor, units of leather, and units of wool). The unit costs of these resources are $5 per hour of labor, $7 per unit of leather, and $3 per unit of wool. In each production cycle, the company has 1000 hours of labor available, 800 units of leather, and 900 units of wool. To avoid inventory surplus at the end of the production cycle, the sales department has set maximum production limits for each jacket type, stipulating that no more than 200 jackets of type 1, 100 jackets of type 2, and 150 jackets of type 3 should be produced. The company aims to determine the optimal production plan for the next production cycle to maximize total profit, while adhering to the constraints of resource availability and production limits.
|
|
Type 1 |
Type 2 |
Type 3 |
|
Labor time required (hours) |
3 |
2 |
2 |
|
Leather (units) |
3 |
2 |
0.5 |
|
Wool (units) |
0.5 |
2 |
3 |
|
Sale price ($/jacket) |
$50 |
$38 |
$29 |
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