Chapter 15

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 12 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3. RMCs 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.

1. a- (10 points) Is it possible for management to achieve both P1 level goals given the constraints on the amounts of each material available? Explain.
2. b- (10points)Treatingtheamountsofeachmaterialavailableas constraints, formulate a goal programming model to determine the optimal product mix. Assume that both P1 priority level goals are equally important to management.
3. c- (10 points) Use the graphical goal programming procedure to solve the model formulated in part (b).
4. d- (10points)Ifgoal1istwiceasimportantasgoal2,whatisthe optimal product mix?