Photo Chemicals produces two types of photograph-developing fluids. Both products cost Photo Chemicals $1 per gallon to produce. Based on an analysis of current inventory levels and outstanding orders for the next month, Photo Chemicals managers have specified that at least 30 gallons of product 1 and at least 20 gallons of product 2 must be produced during the next two weeks. They have also stated that an existing inventory of highly perishable raw material required in the production of both fluids must be used within the next two weeks. The current inventory of the perishable raw material is 80 pounds. Although more of this raw material can be ordered if necessary, any of the current inventory that is not used within the next two weeks will spoil hence the management requirement that at least 80 pounds be used in the next two weeks. Furthermore, it is known that product 1 requires 1 pound of this perishable raw material per gallon and product 2 requires 2 pounds per gallon. Since the firm’s objective is to keep its production costs at the minimum possible level, the managers are looking for a minimum-cost production plan that uses all the 80 pounds of perishable raw material and provides at least 30 gallons of product 1 and at least 20 gallons of product 2.
Develop a linear programming model.