RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended 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 ton of material 3. A ton of solvent base is a mixture of ½ 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 20 tons of material 1, 5 tons of material 2, and 21 tons of material 3 that are available for production. Assuming that RMC is interested in maximizing the total profit contribution, answer the following: a. Find the optimal solution. How many tons of each product should be produced, and what is the projected total profit contribution? b. Is there any unused material? If so, how much? c. Are there any redundant constraint? If so, which
RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended 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 ton of material 3. A ton of solvent base is a mixture of ½ 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 20 tons of material 1, 5 tons of material 2, and 21 tons of material 3 that are available for production. Assuming that RMC is interested in maximizing the total profit contribution, answer the following: a. Find the optimal solution. How many tons of each product should be produced, and what is the projected total profit contribution? b. Is there any unused material? If so, how much? c. Are there any redundant constraint? If so, which
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter8: Cost Analysis
Section: Chapter Questions
Problem 5E
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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 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 ton of
material 3. A ton of solvent base is a mixture of ½ 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 20 tons of material 1, 5 tons of material 2, and 21 tons of material 3 that are
available for production. Assuming that RMC is interested in maximizing the total profit
contribution, answer the following:
a. Find the optimal solution. How many tons of each product should be produced, and
what is the projected total profit contribution?
b. Is there any unused material? If so, how much?
c. Are there any redundant constraint? If so, which ones?
d. Suppose RMC discovers a way to increase the profit of solvent base to $60 per ton.
Does this change the optimal solution? If so, how?
e. Suppose that profit for the solvent base is $50 per ton. What is the optimal solution
now? Comment on any special characteristics that may exist with this profit for the
solvent base.
f. Use the graphical sensitivity analysis approach to determine what ranges of values for
the profit per ton of the fuel additive ad solvent base can exist without causing RMC to
change from the current optimal solution of 25 tons of fuel additive and 20 tons of
solvent base.
g. Determine what happens if an additional 3 tons of material 3 become available. What
is the corresponding dual price?
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