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 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.

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 1: 20 tons
- Raw Material 2: 5 tons
- Raw Material 3: 21 tons

Assuming that RMC is interested in maximizing the total profit contribution, do the following:

1. Develop the linear programming model for this problem.
2. Solve this model using the graphical solution procedure.

Note:
- \(X_2\) increments top to bottom (50, 45, 40, 35, 30, 25, 20, 15, 10, 5, 0)
- \(X_1\) increments left to right (0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50)