Each week, Stockco produces two products. Relevant information for each product is shown in the file P09_05.xlsx. Stockco has a goal of $48 in weekly profit and incurs a $1 penalty for each dollar it falls short of this goal. A total of 32 hours of labor are available. A

$2 penalty is incurred for each hour of overtime (labor over 32 hours) used, and a $1 penalty is incurred for each hour of available labor that is unused. Marketing considerations require that at least 7 units of product 1 be produced and at least 10 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: Avoid underuse of labor.

■ Goal 2: Meet demand for product 1.

■ Goal 3: Meet demand for product 2.

■ Goal 4: Do not use any overtime.

Use goal programming to determine an optimal production schedule.