Hi-Tech Incorporated is a small company that produces three products daily: (1) CD players, (2) cell phones, and (3) photograph cameras. The company has a limited amount of resources used in the production of these products. The limited resources are labor, machine hours, and inventory space allocated to all products. Hi-Tech has 1,560 labor hours per day, 1,900 machine hours per day, and 1,400 square feet of storage space capacity availability to store the three different products each day. In addition, the management policies of the company dictate the following:

The minimum number of cell phones produced needs to be at least 20 percent of all units produced for all three products.

The minimum number of CD players produced needs to be at least 40 percent of all units produced for all three products.

Given the above resource requirements, Hi- Tech Incorporated has the following resource requirements for production and profit for each product being produced.

Resource Requirement

Product	Labour hours	Machine hours	Storage Space	Profit Per unit
CD Player	1	1.25	0.5	27
Cell Phones	5	5	4.5	55
Photograph cameras	3	3.5	2.5	80

a. If Hi-Tech's goal is to maximize the profit, what would be the production quantity of each product and the total profit?

b. Instead of a single objective of maximizing profit, the company has listed the following objectives in order of importance:

1. The owner of Hi-Tech, Donald Schroeder, wants to be able to provide a stable environment for his employees. In order to accomplish his goal of having a stable workforce, he does not want to use fewer than 1,560 hours of labor per day.

2. Hi- Tech would like to achieve a satisfactory daily profit level of $32,000.

3. Donald Schroeder also is concerned about the machine utilization at his company. He wants to be able to effectively utilize the machine hours. In order to reach his goal of high machine utilization, he would like a utilization of at least 1,900 machine hours.

4. Hi- Tech does not want to utilize more than 1,400 square feet of inventory space available.

5. Because Mr. Schroeder has to pay overtime, and due to high overhead costs when the plant is kept open past the normal operating hours, he wants to minimize the amount of overtime by its employees.

6. Due to warehouse space regulations, the company cannot produce more than 180 cell phones per day.

7. If the company can meet the restrictions on manufacturing cell phones specified in objective 6, the company also would like to limit the production of cameras in the following way: Due to warehouse space regulations, the company wants to limit the production of photograph cameras to 220 units per day.

Formulate and solve the goal programming problem and comment on the goals achieved and the goals not achieved.

c. Mr. Schroeder has accepted the fact that some overtime may be unavoidable. He revised the fifth priority goal such that overtime may be limited to 20 hours per day. How will the formulation in part b change? Solve the resulting goal programming problem. How is the solution different than the solution in part b?