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10 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 3 ton of material 3. A ton of solvent base is a mixture of ton of material 1,1 ton of material 2, and ton of material 3. Kashif's production is constrained by a limited availability of the 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? O Yes. It is possible to satisfy both P, level goals. O No. There is an insufficient amount of Material 1. O 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, x, be the number of tons of solvent base produced, d 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 X Check which variable(s) should be in your answer. s.t. Material 1₁+20 2x₂5 55 Material 2 Material 3 ₁+2₂5 21

10 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 3 ton of material 3. A ton of solvent base is a mixture of ton of material 1,1 ton of material 2, and ton of material 3. Kashif's production is constrained by a limited availability of the 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? O Yes. It is possible to satisfy both P, level goals. O No. There is an insufficient amount of Material 1. O 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, x, be the number of tons of solvent base produced, d 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 X Check which variable(s) should be in your answer. s.t. Material 1₁+20 2x₂5 55 Material 2 Material 3 ₁+2₂5 21

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Goal 1 Goal 2 Check the plus and minus signs of all terms and/or values. X Check which variable(s) should be in your answer. X₁ dni pi≥ 0, for i = 1, 2 (c) Use the graphical goal programming procedure to find the optimal solution for the model formulated in part (b). (x₁x₂) = 30,10 (d) If goal 1 is twice as important as goal 2, what is the optimal product mix? (X₁ X₂) = 27.5,15
Transcribed Image Text:Goal 1 Goal 2 Check the plus and minus signs of all terms and/or values. X Check which variable(s) should be in your answer. X₁ dni pi≥ 0, for i = 1, 2 (c) Use the graphical goal programming procedure to find the optimal solution for the model formulated in part (b). (x₁x₂) = 30,10 (d) If goal 1 is twice as important as goal 2, what is the optimal product mix? (X₁ X₂) = 27.5,15
1 ton of material 1 ton of material 2, and 11/13 3 10 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 3 ton of material 3. A ton of solvent base is a mixture of // Kashif's production is constrained by a limited availability of the 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 P₁ 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 P₁ level goals. O No. There is an insufficient amount of Material 1. O 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 P₁ priority level goals are equally important to management. (Let x₁ be the number of tons of fuel additive produced, x₂ be the number of tons of solvent base produced, do, 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 X Check which variable(s) should be in your answer. s.t. Material 1 x₁ + 1/2x₂2≤20 Material 2x₂5 Material 3x₁ + ton of material 3. 102 21
Transcribed Image Text:1 ton of material 1 ton of material 2, and 11/13 3 10 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 3 ton of material 3. A ton of solvent base is a mixture of // Kashif's production is constrained by a limited availability of the 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 P₁ 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 P₁ level goals. O No. There is an insufficient amount of Material 1. O 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 P₁ priority level goals are equally important to management. (Let x₁ be the number of tons of fuel additive produced, x₂ be the number of tons of solvent base produced, do, 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 X Check which variable(s) should be in your answer. s.t. Material 1 x₁ + 1/2x₂2≤20 Material 2x₂5 Material 3x₁ + ton of material 3. 102 21
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