A manager of a small fabrication plant must decide on a production schedule of two new products for the automobile industry. The unit profit is $20 for product 1 and $70 for product 2.

The manufacture of these products depends largely on the availability of certain subassemblies the plant receives daily from a local distributor. It takes two of these subassemblies for each unit of product 1 and also two for each unit of product 2. Twenty such subassemblies are delivered daily.

Further, it takes four hours to make a unit of product 1 and six hours to make a unit of product 2. The plant has assigned only six workers, each one with an 8-hour shift, for these new products. Due to limited demand, the manager does not want more than six units of product 2 produced daily.

1) Formulate this problem as a math program.

2) Solve graphically for the optimal solution. Describe the optimal solution.

3) What is the profit generated by using the above optimal solution?

After you finish with this problem, you received a memo from the accounting department. According to the accountant, the revised unit profit is $30 for product 1 and $40 for product 2 based on the new marketing information.

4) What will be your modified optimal solution based on the information from the accountant?

5) What is the modified profit?