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RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) 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 % ton of material 1, % ton of material 2, and %0 ton of material 3. After deducting relevant costs, the profit contribution is P2000 for every ton of fuel additive produced and P1500 for every ton of solvent base produced. RMC's production is constrained by a limited availability of the three raw materials. Forthe current production period, RMChas the following available quantities of each raw material: Amount Available for Production Raw Material Material 1 Material 2 Material 3 20 tons 5 tons 21 ton Assuming that RMC is interested in maximizing the total profit contribution, answer the following: į. Compute the value of the objective function when 1 ton is added to the amount available for production of raw material 1. Also, find the corresponding dual price k. Compute the range where the dual price computed in () remains valid. I. Compute the range of optimality for the objective function coefficients.

RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) 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 % ton of material 1, % ton of material 2, and %0 ton of material 3. After deducting relevant costs, the profit contribution is P2000 for every ton of fuel additive produced and P1500 for every ton of solvent base produced. RMC's production is constrained by a limited availability of the three raw materials. Forthe current production period, RMChas the following available quantities of each raw material: Amount Available for Production Raw Material Material 1 Material 2 Material 3 20 tons 5 tons 21 ton Assuming that RMC is interested in maximizing the total profit contribution, answer the following: į. Compute the value of the objective function when 1 ton is added to the amount available for production of raw material 1. Also, find the corresponding dual price k. Compute the range where the dual price computed in () remains valid. I. Compute the range of optimality for the objective function coefficients.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 73P
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RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) 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 % ton of material 1, % ton of material 2, and % ton of material 3. After deducting relevant costs, the profit contribution is P2000 for every ton of fuel additive produced and P1500 for every ton of solvent base produced. RMC's production is constrained by a limited availability of the three raw materials. Forthe current production period, RMChas the following available quantities of each raw material: Amount Available for Production Raw Material 20 tons 5 tons 21 ton Material 1 Material 2 Material 3 Assuming that RMC is interested in maximizing the total profit contribution, answer the following: į. Compute the value of the objective function when 1 ton is added to the amount available for production of raw material 1. Also, find the corresponding dual price k. Compute the range where the dual price computed in () remains valid. I. Compute the range of optimality for the objective function coefficients.
Transcribed Image Text:RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) 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 % ton of material 1, % ton of material 2, and % ton of material 3. After deducting relevant costs, the profit contribution is P2000 for every ton of fuel additive produced and P1500 for every ton of solvent base produced. RMC's production is constrained by a limited availability of the three raw materials. Forthe current production period, RMChas the following available quantities of each raw material: Amount Available for Production Raw Material 20 tons 5 tons 21 ton Material 1 Material 2 Material 3 Assuming that RMC is interested in maximizing the total profit contribution, answer the following: į. Compute the value of the objective function when 1 ton is added to the amount available for production of raw material 1. Also, find the corresponding dual price k. Compute the range where the dual price computed in () remains valid. I. Compute the range of optimality for the objective function coefficients.
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