Joseon, 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, 15 ton of material 2, and 310 ton of material 3. After deducting relevant costs, the profit contribution is P2000 for every ton of fuel additive produced and P1500 for every ton of solvent base produced.

Joseon's production is constrained by a limited availability of the three raw materials. For the current production period, Joseon has the following available 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 Joseon is interested in maximizing the total profit contribution, answer the following:

a. Is there any unused material? If so, how much?

b. Are any of the constraints redundant? If so, which one? c. Identify the binding constraint/s: ___________________________________________________________________ d. Identify the non-binding constraint/s: ___________________________________________________________________ e. Compute the value of the objective function when 1 ton is added to the original amount available for production of raw material 1. Also, find the corresponding dual price dual price. f. Compute the range where the dual price computed in (i) remains valid. g. Compute the range of optimality for the objective function coefficients.