Formulate an optimization model (decision variables, objective function, and constraints) to help the company identify the optimal production plan. b) Solve the model using Lingo/Excel and explain the results obtained in the booklet
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) (see the table below). The unit costs of
these resources are $5 per hour of labor, $7 per unit of leather, and $3 per unit of wool. In each production
cycle, the company has 1000 hours of labor available, 800 units of leather, and 900 units of wool.
To avoid inventory at the end of the production cycle, the sales department has set maximum production
limits for each jacket type (i.e., no more than that should be produced): 200 jackets of type 1, 100 jackets
of type 2, and 150 jackets of type 3. The company wants to determine the optimal production plan for the next production cycle that maximizes total profit, subject to the resource availability and production limits.
| Type 1 | Type 2 | Type 3 | |
| Labor time required (hours) | 3 | 2 | 2 |
| Leather (units) | 3 | 2 | 0.5 |
| Wool (units) | 0.5 | 2 | 3 |
| Sale price ($/jacket) | $50 | $38 | $29 |
a) Formulate an optimization model (decision variables, objective function, and
constraints) to help the company identify the optimal production plan.
b) Solve the model using Lingo/Excel and explain the results obtained in the booklet
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