Based on Vasko et al. (1987). Bethlehem Steel can fill orders using five different types of steel molds. Up to three different molds of each type can be purchased.

Each individual mold can be used to fill up to 100 orders per year. Six different types of orders must be filled during the coming year. The waste (in tons) incurred if a type of mold is used to fill an order is shown in the file P09_18.xlsx (where an “x” indicates that a type of mold cannot be used to fill an order).

The number of each order type that must be filled during the coming year is also shown in this file.

Bethlehem Steel has the following two goals, listed in order of priority.

■ Goal 1: Because molds are very expensive, Bethlehem wants to use at most five molds.

■ Goal 2: Bethlehem wants to have at most 600 tons of total waste.

Use goal programming to determine how Bethlehem should fill the coming year’s orders.