Blending Problem to Maximize Profits. 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 ton of fuel additive is a mixture of 2/5 ton of material 1 and 3/5 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. RMCs production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material: Raw Material Amount Available for Production Material 1 20 tons Material 2 5 tons Material 3 21 tons Assuming that RMC is interested in maximizing the total profit contribution, answer the following. a. What is the linear programming model for this problem and the optimized solution?

\begin{tabular}{|c|c|c|c|c|c|c|c|} \hline & Fuel Additive & Solvent Base & & & & & \\ \hline \multirow[t]{3}{*}{ Unit Profit (per ton) } & & & & & & Range Name & Cells \\ \hline & & & Resources & & Resources & Production & B11:C11 \\ \hline & \multicolumn{2}{|c|}{ Resource Requirements } & Used & & Available & ResourcesUsed & D6:D8 \\ \hline Material 1 & & & &