An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 5

RMC Corporation blends three raw materials to produce two products: a fuel additive and a solvent base. Bach 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 P 1 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 P 1 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 P 1 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?