MC, 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 fued addi nd a solvent base. Each ton of fucl additive is a mixture of 2/5 ton of material 1 and 3/5 of materlal 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of material 2 , and on 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. MMC's production is constrained by a limited availability of the three raw materials, For the current production period, RMC has avaliable the folowing quantities of each raw matersh Assuming that RMC is interested in maximizing the total profit contribution, answer the following. (Assume F is the number of tons of fuel addilive and S is the number of tons of solvent base.) (a) What is the linear programming model for this problem that maximizes profit (in dollars)? (b) Find the optimal solution using the graphical solution procedure. How many tons of each product should be produced? (F,S)=(xx) What is the projected total profit contribution (in dollars)? (c) Is there any unused material? If so, how much (in tons)? (If there is no unused material, enter 0 .) Material 1 tons Material 2 tons Material 3 tons