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 ton of material 3. A ton of solvent base is a mixture of ton of material 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 10 quantities of each raw material: material 1, 20 tons; material 2, 5 tons; material 3, 21 tons. Management wants to achieve the following P₁ priority level goals. 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? Goal 1: Produce at least 30 tons of fuel additive. Goal 2: Produce at least 15 tons of solvent base. O Yes. It is possible to satisfy both P₁ level goals. O No. There is an insufficient amount of Material 1. No. There is an insufficient amount of 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 P₁ 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, dp, 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 s.t.
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 ton of material 3. A ton of solvent base is a mixture of ton of material 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 10 quantities of each raw material: material 1, 20 tons; material 2, 5 tons; material 3, 21 tons. Management wants to achieve the following P₁ priority level goals. 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? Goal 1: Produce at least 30 tons of fuel additive. Goal 2: Produce at least 15 tons of solvent base. O Yes. It is possible to satisfy both P₁ level goals. O No. There is an insufficient amount of Material 1. No. There is an insufficient amount of 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 P₁ 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, dp, 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 s.t.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 33P: Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand...
Related questions
Question
Transcribed Image Text: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 ton of material 3. A ton of solvent base is a
5
1/1/₁
1/1/3
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
10
quantities of each raw material: material 1, 20 tons; material 2, 5 tons; material 3, 21 tons. Management wants to achieve the following P₁ priority level goals.
mixture of
ton of material 1,
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.
No. There is an insufficient amount of Material 2.
O No. There is an insufficient amount of Material 3.
Min
Goal 1: Produce at least 30 tons of fuel additive.
Goal 2: Produce at least 15 tons of solvent base.
(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.)
s.t.
Material 1
Material 2
Material 3
Goal 1
Goal 2
Transcribed Image Text:Xidni 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).
(x₁₁x₂) =
(d) If goal 1 is twice as important as goal 2, what is the optimal product mix?
(x₁₁x₂) = 1
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 8 images
Recommended textbooks for you
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,