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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 2/5 ton of material 1 and 3/5 of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced. RMC's production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material: Raw Material Amount Available for Production Material 1 Material 2 Material 3 38 tons 11 tons 39 tons Assuming that RMC is interested in maximizing the total profit contribution, answer the following. (Assume F is the number of tons of fuel additive and S is the number of tons of solvent base.)

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 2/5 ton of material 1 and 3/5 of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced. RMC's production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material: Raw Material Amount Available for Production Material 1 Material 2 Material 3 38 tons 11 tons 39 tons Assuming that RMC is interested in maximizing the total profit contribution, answer the following. (Assume F is the number of tons of fuel additive and S is the number of tons of solvent base.)

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 2/5 ton of material 1 and 3/5 of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced. RMC's production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material: Raw Material Amount Available for Production a. Material 1 Material 2 Material 3 38 tons 11 tons 39 tons Assuming that RMC is interested in maximizing the total profit contribution, answer the following. (Assume F is the number of tons of fuel additive and S is the number of tons of solvent base.) Is there any unused material? If so, how much (in tons)? Using this information, determine if any of the constraints are redundant. If so, which ones?
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 2/5 ton of material 1 and 3/5 of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced. RMC's production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material: Raw Material Amount Available for Production a. Material 1 Material 2 Material 3 38 tons 11 tons 39 tons Assuming that RMC is interested in maximizing the total profit contribution, answer the following. (Assume F is the number of tons of fuel additive and S is the number of tons of solvent base.) Is there any unused material? If so, how much (in tons)? Using this information, determine if any of the constraints are redundant. If so, which ones?
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