Problem: 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 mixture of ½ ton of material 1, 1/5 ton of material 2, and 3/10 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 limited availability of the three raw materials. For the current production period, RMC has available 20 tons of raw material 1, 5 tons of raw material 2, and 21 tons of raw material
Assuming that RmC is maximizing the total profit contribution answer the following:
Q1. What is the linear programming model for this problem
Q2. Find the optimal solution using the graphical solution procedure. How many tons of each product should be produced and what is the project total profit contribution?
Q3. Is there any unused material. If so how mch?
Q4. Are there any redundant contraints? If so, which ones?