Question

Please turn in the following problem. No need to solve the LP.

Exercise 2 (Production quantity planning)

P3 is a small firm that produces a variety of chemical products. In a particular production process, three raw materials (#1, #2, and #3) are blended to produce two products: a fuel addictive and a solvent. Each ton of fuel addictive is a mixture of 0.4 ton of material 1 and 0.6 ton of material 3. A ton of solvent is a mixture of 0.5 ton of material 1, 0.2 ton of material 2, and 0.3 ton of material 3. After deducting relevant costs, the gross profit margin is $40 for each ton of fuel addictive and $30 for each ton of solvent.

P3's production is constrained by a limited availability of the three raw materials. For the current period, P3 has the following quantities on hand:

Material 1 20 tons

Material 2 5 tons

Material 3 21 tons

Develop a linear program to determine the optimal production quantities for fuel addictive and solvent. Use x1 and x2 to denote the production quantities for fuel addictive and solvent, respectively.

(PLEASE INCLUDE STEPS TO WORK OUT PROBLEM)

Answer 1