ABC, Inc. produces three types of tables. Manufacturing one unit of table type 1 (Table 1) requires 5 cutting hours, 1 assembly hour and 2 painting hours. Manufacturing one unit of table type 2 (Table 2) requires 2 cutting hours, 4 assembly hours, and 1 painting hour. Manufacturing one unit of table type 3 (Table 3) does not require any cutting hours but it does require 1 assembly hour and 6 painting hours. The company has 200 hours available for cutting, 100 hours for assembly and 200 hours for painting in the following week. Mr. Wood, manager of ABC Inc., estimates that one unit of Table 1 will yield a profit of $50, Table 2 a profit of $15 and Table 3 a profit of $10.

Write an LP formulation (definitions of your decision variables, the objective function and all the necessary constraints) to maximize total weekly profit. Then prepare a pyomo model to solve it and prepare a sensitivity report. You will answer the sensitivity questions using the sensitivity report. Answer the following questions:

1. If additional assembly hours were available at a cost of $10/hour, how many additional hours would you recommend purchasing? Why?

2. Mr. Wood just received the news that a painter has fallen sick and he will not be able to work at all next week. Normally, he works 40 hours in a week. How would that affect the total profit?

3. Mr. Wood was disappointed to see that the computer solution did not recommend manufacturing any of Table 2. Looking at the long term, he believes that closing this line of product would not be a good strategy. If he decides to manufacture Table 2, what unit profit of Table 2 would justify manufacturing it?

4. If Table 1 yields a profit of $40/unit, how would the optimal solution and total profit be affected?