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 25 ton of material 1 and 35 of material 3. A ton of solvent base is a mixture of 12 ton of material 1, 1/5 ton of material 2, and 310 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 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	38 tons
Material 2	11 tons
Material 3	39 tons

Assuming that RMC is interested in maximizing the total profit contribution, answer the following. (Assume F is the number of tons of fuel additive 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)?

Max: ____

s.t.

Material 1 ____

Material 2 ____

Material 3____

F, S 0

(b)

Find the optimal solution using the graphical solution procedure. How many tons of each product should be produced?

(F, S) = ____

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

(d)

Are any of the constraints redundant? If so, which ones? (Select all that apply.)

Material 1 constraint

Material 2 constraint

Material 3 constraint

No redundant constraints