A firm can manufacture dresses or shirts. The inputs required for these operations are labor, machines, and cotton, and the input coefficients for the two processes for each of the three inputs are as follows:
|
|
Labor
|
Machines
|
Cottons
|
|
Dresses
|
10
|
40
|
20
|
|
Shirts
|
10
|
10
|
5
|
The prices of the finished articles are $12 and $6 respectively (dresses, shirts). The firm has available 100 units of labor, 160 machines, and 100 units of cotton.
- Write down the revenue maximizing linear programming problem for the firm.
- Sketch the opportunity set for the firm. Is this set convex?
- At what levels should the firm operate the two processes (dresses & shirts) to achieve maximum revenue? Explain how you arrived at your solution.
- Is there any other combination of output levels which will generate that maximum revenue? (That is, is your solution unique?) Explain.
- Which resource will not be fully utilized at the optimum? How do you know? Which resources will not be fully utilized at the optimum? How do you know?
- What would the prices of dresses have to rise to for the firm to stop manufacturing shirts altogether? (Assuming everything else in the problem remains the same.)