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 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?