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 2 1 3 5 mixture of ton of material 1 and ton of material 3. A ton of solvent base is a mixture of ton of material 1, ——33 ton of material 2, and 5 10 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, 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 P₁ 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 P₁ level goals. Goal 1: Produce at least 30 tons of fuel additive. Goal 2: Produce at least 15 tons of solvent base. O No. There is an insufficient amount of Material 1. O 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 x₁ 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 dni be the deviation variable which is less than the value of goal i, for i = 1, 2.) Min s.t. Material 1 Material 2 Material 3 Goal 1 Goal 2 Xirdni dpi 2 0, for i = 1, 2 (c) Use the graphical goal programming procedure to find the optimal solution for the model formulated in part (b). (x₁, x₂) = (d) If goal 1 is twice as important as goal 2, what is the optimal product mix? (x₁, x₂) =
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 2 1 3 5 mixture of ton of material 1 and ton of material 3. A ton of solvent base is a mixture of ton of material 1, ——33 ton of material 2, and 5 10 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, 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 P₁ 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 P₁ level goals. Goal 1: Produce at least 30 tons of fuel additive. Goal 2: Produce at least 15 tons of solvent base. O No. There is an insufficient amount of Material 1. O 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 x₁ 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 dni be the deviation variable which is less than the value of goal i, for i = 1, 2.) Min s.t. Material 1 Material 2 Material 3 Goal 1 Goal 2 Xirdni dpi 2 0, for i = 1, 2 (c) Use the graphical goal programming procedure to find the optimal solution for the model formulated in part (b). (x₁, x₂) = (d) If goal 1 is twice as important as goal 2, what is the optimal product mix? (x₁, x₂) =
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...
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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
1
ton of material 1,
1/1/201
²/3
2
²/3 ton of material 1 and 3³33 - ton of material 3. A ton of solvent base is a mixture of
mixture of
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, 20 tons; material 2, 5 tons; material 3, 21 tons. Management wants to achieve the
following P₁ priority level goals.
Goal 1: Produce at least 30 tons of fuel additive.
Goal 2: Produce at least 15 tons of solvent base.
Min
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.
O No. There is an insufficient amount of Material 3.
s.t.
(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, dp, be the deviation variable which exceeds the value of goal i, and dni be the deviation
variable which is less than the value of goal i, for i = 1, 2.)
Material 1
Material 2
Material 3
Goal 1
Goal 2
Xirdni dpi 20, for i = 1, 2
ton of material 2, and
3
10
(c) Use the graphical goal programming procedure to find the optimal solution for the model formulated in part (b).
(x₁, x₂) =
(d) If goal 1 is twice as important as goal 2, what is the optimal product mix?
(
(x₁, x₂) =
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