Problem 14-01 (Algorithmic) 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 1/4 ton of material 1 and 3/4 ton of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/8 ton of material 2, and 3/8 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, 15 tons; material 2, 3 tons; material 3, 30 tons. Management wants to achieve the following P1 priority level goals: Goal 1: Produce at least 32 tons of fuel additive. Goal 2: Produce at least 16 tons of solvent base. Assume there are no other goals. a. Is it possible for management to achieve both P level goals given the constraints on the amounts of each material available? Explain. Amount needed to Raw Material Achieve Both P Goals 1 16 2 2 3 30 Since there are only 15 tons of Material 1 available, it is not possible d. If goal 1 is twice as important as goal 2, choose the correct graph for the optimal product mix? (1) (ii) 90- Goal 1 80 Material 3 70+ 60+ 50+ 40+ 30 Material 1 20- 10- 10 0 20 30 40 Material 2 Goal 2 (33, 13) + 50 60 21 90- 80- 70+ 60- 50 40+ 30 Material 1 20- 10- 0 Material 3 6- 10 (28, 16) 20 30 Goal 1 40 Material 2 50 Goal 2 60 21 (iii) 30- 80 70+ 60+ 50+ 40+ 30 Material 1 20- 10- + 0 10 Graph (iii) Material 3 (12, 24) 6- 20 30 Goal 1 40 Material 2 50 Goal 2 60 21 (iv) 230- 80 70+ 60+ 50- 40+ 30 Material 1 20- 10- 4 0 Material 3 9 10 (32, 14) + 20 30 Goal 1 40 Material 2 + 50 Goal 2 60 x1