Stockco fills orders for three products for a local warehouse.

Stockco must determine how many of each product should be ordered at the beginning of the current month. This month, 400 units of product 1, 500 units of product 2, and 300 units of product 3 will be demanded. The cost and space taken up by one unit of each product are shown in the file P16_34.xlsx. If Stockco runs out of stock before the end of the month, the stockout costs also shown in this file are incurred.

Stockco has $17,000 to spend on ordering products and has 3700 square feet of warehouse space. A $1 penalty is assessed for each dollar spent over the budget limit, and a $10 cost is assessed for every square foot of warehouse space needed.

a. Determine Stockco’s optimal ordering policy.

b. Suppose that Stockco has set the following goals, listed in order of priority:

■ Goal 1: Spend at most $17,000.

■ Goal 2: Use at most 3700 square feet of warehouse space.

■ Goal 3: Meet demand for product 1.

■ Goal 4: Meet demand for product 2.

■ Goal 5: Meet demand for product 3.

Develop a goal programming model for Stockco.