Show the complete solution (drop the formula used if there is). Kindly show it clearly

XYZ, 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 kg of fuel additive is a mixture of kg of material 1 and of material 3. A kg of solvent base is a mixture of kg of material 1, kg of material 2, and kg of material 3. After deducting relevant costs, the profit contribution is P20 for every kg of fuel additive produced and P15 for every kg of solvent base produced.

XYZ's production is constrained by a limited availability of the three raw materials. For the current production period, XYZ has the following available quantities of each raw material:

Raw Material	Amount Available for Production
Material 1	20 kg
Material 2	5 kg
Material 3	21 kg

Assuming that XYZ is interested in maximizing the total profit contribution, answer the following:

a. Define the variables used and formulate the linear programming model (with no fractions) for this problem.

b. Graph the constraints and identify the feasible region.

c. Complete the table on corner points and their z-values.

d. How many kg of each product should be produced, and what is the projected total profit contribution?

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

f. Are any of the constraints redundant? If so, which one?

g. Identify the binding constraint/s:

h. Identify the non-binding constraint/s:

i. Compute the value of the objective function when 1 kg is added to the original amount available for production of raw material 1. Also, find the corresponding dual price.

j. Compute the range where the dual price computed in (i) remains valid.

k. Compute the range of optimality for each of the objective function coefficients if the other is kept constant.