A company manufactures cars and trucks. Each vehicle must be processed in the paint shop and body assembly shop. If the paint shop were only painting trucks then 40 per day could be painted. If the paint shop were only painting cars, then 60 per day could be painted. If the body shop were only producing trucks, then it could process 50 per day. Same for the cars (50 per day). Each truck contributes $300 to profit and each car contributes $200 to profit.

a. Formulate the problem to determine a daily production schedule that will maximize the company’s profit (write your decision variables, objective function and constraints).

b. Use linear programming (LP) graphical method to determine a daily production schedule that will maximize the company’s profit.

c. Suppose that auto dealers require that the auto company produce at least 30 trucks and 20 cars. How will the feasible region change? Explain on the new graph and find the optimal solution to this new LP.

d. The capacity of the paint shop will be doubled next year. Formulate the problem for t next year now and evaluate the change in terms of objective function value and the production schedule (i.e., after you solve the problem for this year, you solve it again for next year given the new capacity in the paint shop and compare the objective function values and production schedules) – do not consider the condition given in part c.