Each week, Stockco produces two products. Relevant information for each product is shown in the file P16_05.xlsx. Stockco has a goal of $4800 in weekly profit and incurs a $1 penalty for each dollar...

Each week, Stockco produces two products. Relevant information for each product is shown in the file P16_05.xlsx. Stockco has a goal of $4800 in weekly profit and incurs a $1 penalty for each dollar it falls short of this goal. A total of 3200 hours of labor are available. A $2 penalty is incurred for each hour of overtime (labor over 3200 hours) used, and a $1 penalty is incurred for each hour of available labor that is unused. Marketing considerations require that at least 700 units of product 1 be produced and at least 1000 units of product 2 be produced. For each unit (of either product) by which production falls short of demand, a penalty of $5 is assessed.

a. Determine how to minimize the total penalty incurred by Stockco.

b. Suppose the company sets (in order of importance) the following goals:

■ Goal 1: Make the required profit.

■ Goal 2: Avoid underuse of labor.

■ Goal 3: Meet demand for product 1.

■ Goal 4: Meet demand for product 2.

■ Goal 5: Do not use any overtime.

Use goal programming to determine an optimal production schedule.