Beta company produces two kinds of fancy products—table lamp and key chain. Production of either a table lamp or key chain requires 0.5 hour of production capacity in the plant. The plant has a maximum production capacity of 15 hours per week. Because of the limited sales capacity, the maximum number of table lamps and key chains that can be sold are 18 and 25 per week, respectively. The gross margin from the sale of a table lamp is Z 60 and Z 30 for a key chain.

The overtime hour should not exceed 5 hours/week.

The plant manager has set the following goals arranged in the order of importance. 1. He wants to avoid any underutilization of production capacity. 2. He wants to limit the overtime hours to 5 hours. 3. He wants to sell as many table lamps and key chains as possible. Since, the gross margin from the sale of a table lamp is set at twice the amount of profit from a key chain, he has twice as much desire to achieve the sales goal for table lamps as for key chains.

4.

He wants to minimize the overtime operation of the plant as much as possible.

Formulate this as a goal programming problem.