Y9 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 33 tons Material 2 9 tons Material 3 36 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.) (a) What is the linear programming model for this problem that maximizes profit (in dollars)?} Max Material1 Material2 Material3 (b) Find the optimal solution using the graphical solution procedure. How many tons of each product should be produced? (F, S) What is the projected total profit contribution (in dollars)? $ (c) Is there any unused material? If so, how much (in tons)? (If there is no unused material, enter 0.) Material 1 tonsMaterial 2 tonsMaterial 3 tons (d) Are any of the constraints redundant? If so, which ones? (Select all that apply.) Material 1 constraintMaterial 2 constraintMaterial 3 constraint No redundant constraints
Y9
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 | 33 tons |
| Material 2 | 9 tons |
| Material 3 | 36 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.)
(a)
What is the linear programming model for this problem that maximizes profit (in dollars)?}
Max
Material1
Material2
Material3
(b)
Find the optimal solution using the graphical solution procedure. How many tons of each product should be produced?
(F, S)
What is the projected total profit contribution (in dollars)?
$
(c)
Is there any unused material? If so, how much (in tons)? (If there is no unused material, enter 0.)
Material 1 tonsMaterial 2 tonsMaterial 3 tons
(d)
Are any of the constraints redundant? If so, which ones? (Select all that apply.)
Material 1 constraintMaterial 2 constraintMaterial 3 constraint No redundant constraints
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