Industrial Chemicals produces two adhesives used in the manufacturing process for airplanes. The two adhesives, which have different bonding strengths, require different amounts of production time: the IC-100 adhesive requires 20 minutes of production time per gallon of finished product, and the IC-200 adhesive uses 30 minutes of production time per gallon. Both products use 1 pound of a highly perishable resin for each gallon of finished product. Inventory currently holds 300 pounds of the resin, and more can be obtained if necessary. However, because of the limited shelf life of the material, any amount not used in the next two weeks will be discarded. The firm has existing orders for 100 gallons of IC-100 and 120 gallons of IC-200. Under normal conditions, the production process operates eight hours per day, five days per week. Management wants to schedule production for the next two weeks to achieve the following goals:

Priority Level 1 Goals

Goal 1: Avoid underutilization of the production process.

Goal 2: Avoid overtime in excess of 20 hours for the two weeks.

Priority Level 2 Goals

Goal 3: Satisfy existing orders for the IC-100 adhesive; that is, produce at least 100 gallons of IC-100.

Goal 4: Satisfy existing orders for the IC-200 adhesive; that is, produce at least 120 gallons of IC-200.

Priority Level 3 Goal

Goal 5: Use all the available resin.

a. Formulate a goal programming model for the Industrial Chemicals problem. Assume that both priority level 1 goals and both priority level 2 goals are equally important.

b. Use the graphical goal programming procedure to develop a solution for the model formulated in part (a).