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 kilo of fuel additive is a mixture of 0.4 kilos of material 1 and 0.6kilos of material 3. A kilo of solvent base is a mixture of 0.5kilos of materials 1, 0.2 kilos of materials 2 and 0.3kilos of material 3. After deducting relevant costs, the profit contribution is 40 for every kilo of fuel additive produced and 30 for every kilo of solvent base produced. RMC`s production is constrained by a limited availability of the three raw materials.

Assuming that RMC is interested in maximising the total profit contribution, 1. answer the following: (a) What is the linear programming model for this problem? (b) Find the optimal solutions using the graphical solutions procedure. How much kilos of each product should be produced, and what is the projected total profit contribution? (c) Is there any unused material? If so, how much? (d) Are there any redundant constraints? If so, which ones?