MATH JKP 3 (USE number in this Question and Make answer clear) DO NOT POST IRRELEVANT WORK HERE!!!

3. [-/9.09 Points] DETAILS ASWMSCI15 14.E.001. MY NOTES ASK YOUR TEACHER 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 ton of material 1 and ton of material 3. A ton 5 of solvent base is a mixture of ton of material 1, ton of material 2, and - ton of material 3. RMC's production is constrained by a limited availability of the three raw materials. For the current 10 production period, RMC has the following quantities of each raw material: material ,20 tons; material 2, 5 tons; material 3, 21 tons. Management wants to achieve the following P, 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 level goals given the constraints on the amounts of each material available? If not, which constraint is the limiting factor? O Yes. It is possible to satisfy both P, level goals. O No. There is an insufficient amount. Material 1. O No. There is an insufficient amount Material 2. O No. There is an insufficient amount of Material 3. (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, priority level goals are equally important to management. (Let x be the number of tons of fuel additive produced, x be the number of tons solvent base produced, do, be the deviation variable which exceeds the value of goal i, and d be the deviation variable which less than the value of goal i, for i = 1, 2.) Min s.t. Material 1 Material 2 Material 3 Goal 1 Goal 1 Goal 2 Xirdni dpi 0, for i = 1, 2 (c) Use the graphical goal programming procedure to find the optimal solution for the model formulated in part (b). (x, x): 1' (d) If goal 1 is twice as important as goal 2, what is the optimal product mix? (X X) = (