The RMC Corporation blends three raw materials to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 2⁄5 ton of material 1 and 3⁄5 ton of material 3. A ton of solvent base is a mixture of 1⁄2 ton of material 1, 1⁄5 ton of material 2, and 3⁄10 ton of material 3. RMC’s production is constrained by a limited availability of the three raw materials. For the current production period, RMC has the following quantities of each raw material: material 1, 20 tons; material 2, 5 tons; material 3, 21 tons. Management wants to achieve the following P1 priority level goals:

Goal 1: Produce at least 30 tons of fuel additive.

Goal 2: Produce at least 15 tons of solvent base.

Assume there are no other goals.

a. Is it possible for management to achieve both P1 level goals given the constraints on the amounts of each material available? Explain.

b. Treating the amounts of each material available as constraints, formulate a goal programming model to determine the optimal product mix. Assume that both P1 priority level goals are equally important to management.

c. Use the graphical goal programming procedure to solve the model formulated in part (b).

d. If goal 1 is twice as important as goal 2, what is the optimal product mix?