1. XYZ, 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 kg of fuel additive is a mixture of 2⁄5 kg of material 1 and 3⁄5 of material 3. A kg of solvent base is a mixture of 1⁄2 kg of material 1, 1⁄5 kg of material 2, and 3⁄10 kg of material 3. After deducting relevant costs, the profit contribution is P20 for every kg of fuel additive produced and P15 for every kg of solvent base produced. XYZ’s production is constrained by a limited availability of the three raw materials. For the current production period, XYZ has the following available quantities of each raw material: Raw Material Amount Available for Production Material 1 20 kg Material 2 5 kg Material 3 21 kg Assuming that XYZ is interested in maximizing the total profit contribution, answer the following: a. Define the variables used and formulate the linear programming model (with no fractions) for this problem b. Graph the constraints and identify the feasible region. c. Complete the table on corner points and their z-values. d. How many kg of each product should be produced, and what is the projected total profit contribution?
1. XYZ, 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 kg of fuel additive is a mixture of 2⁄5 kg of material 1 and 3⁄5 of material 3. A kg of solvent base is a mixture of 1⁄2 kg of material 1, 1⁄5 kg of material 2, and 3⁄10 kg of material 3. After deducting relevant costs, the profit contribution is P20 for every kg of fuel additive produced and P15 for every kg of solvent base produced. XYZ’s production is constrained by a limited availability of the three raw materials. For the current production period, XYZ has the following available quantities of each raw material:
Raw Material Amount Available for Production
Material 1 20 kg
Material 2 5 kg
Material 3 21 kg
Assuming that XYZ is interested in maximizing the total profit contribution, answer
the following:
a. Define the variables used and formulate the linear programming model (with
no fractions) for this problem
b. Graph the constraints and identify the feasible region.
c. Complete the table on corner points and their z-values.
d. How many kg of each product should be produced, and what is the
projected total profit contribution?
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