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 addictive 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 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 availabilty of the three raw materials. For the current production period, RMC has avaialble the following quantities of each raw material.
Raw MaterialAmount Available for Production
1 20 tons
2 5 tons
3 21 tons
Assuming that RMC is interest in maximizing the total profit contribution, do the following:
1. Develop the linear programming model for this problem?
2. Solve this model using the graphical solution procedure.
X2 increments top to bottom (50,45,40,35,30,25,20,15,10,5,0)
X1 increments left to right (0,5,10,15,20,25,30,35,40,45,50)