ton The Kashif Corporation blends three raw materials to produce two products: a fuel additive and...

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ton The Kashif 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 - of material 3. A ton of solvent base is a mixture of 1 ton of material 1, - ton of material 2, and 3 ton of material 3. Kashif's production is constrained by a limited availability of the 10 three raw materials. For the current production period, Kashif 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 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? Yes. It is possible to satisfy both P level goals. No. There is an insufficient amount of Material 1. No. There is an insufficient amount of Material 2. 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, x2 be the number of tons of solvent base produced, dpi be the deviation variable which exceeds the value of goal i, and d; be the deviation variable which is less than the value of goal i, for i = 1, 2.) Min ni s.t. Material 1 2 5x1 20 Material 2 0x1 + x2 5 Material 3 3 3 5x1 + 10*221 Goal 1 1x1 +0x2+ -d + d = 30 Goal 2 did pi Xi'ani' = 0, for 1, 2 (c) Use the graphical goal programming procedure to find the optimal solution for the model formulated in part (b). (x1,x2) 27.5,15 (d) If goal 1 is twice as important as goal 2, what is the optimal product mix? (x1, x2)=30,10 ton The Kashif 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 - of material 3. A ton of solvent base is a mixture of 1 ton of material 1, - ton of material 2, and 3 ton of material 3. Kashif's production is constrained by a limited availability of the 10 three raw materials. For the current production period, Kashif 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 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? Yes. It is possible to satisfy both P level goals. No. There is an insufficient amount of Material 1. No. There is an insufficient amount of Material 2. 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, x2 be the number of tons of solvent base produced, dpi be the deviation variable which exceeds the value of goal i, and d; be the deviation variable which is less than the value of goal i, for i = 1, 2.) Min ni s.t. Material 1 2 5x1 20 Material 2 0x1 + x2 5 Material 3 3 3 5x1 + 10*221 Goal 1 1x1 +0x2+ -d + d = 30 Goal 2 did pi Xi'ani' = 0, for 1, 2 (c) Use the graphical goal programming procedure to find the optimal solution for the model formulated in part (b). (x1,x2) 27.5,15 (d) If goal 1 is twice as important as goal 2, what is the optimal product mix? (x1, x2)=30,10