A chemical manufacturing company produces three types of industrial solvents, S-1, S-2, and S-3. The profits per thousand gallons for the three solvents are $300, $500, and $800 respectively. The production process requires blending and purification. It also requires additional labor for handling the finished products. The company has 260 hours of blending, 300 hours of purification, and 160 labor hours available. The requirements for each solvent are shown in the table below:
S-1 S-2 S-3
Blending (hours/1000gallons) 2 2 3
Purification (hours/1000gallons) 1 2 4
Labor (hours/1000gallons) 1 2 2

1. Formulate a linear program that can be used to determine the optimal product mix for the chemical company. Specifically, do the following: Identify the decision variables (make sure that you specify the units for these variables). Specify the objective function and the relevant constraints.
2. The production manager uses a DSS to obtain the optimal production mix. For this optimal product mix, 250 hours of blending, 300 hours of purification, and 160 hours of labor are required. The maximum attainable profit is desired. Develop a simple DSS prototype to solve this production-planning problem and to confirm the optimal solutions.
a. How many gallons of S-1, S-2, and S-3 are produced under this optimal product mix?
b. What is the maximum attainable profit?
c. What is the profit contribution for each solvent (S-1, S-2, S-3)?

3. Perform sensitivity analysis to determine how much should the manager be willing to pay for:
(a) An additional hour of blending;
(b) An additional hour of purification;
(c) An additional hour of labor.

Write a short memo to the vice-president of production recommending whether the availability of any of the three resources (blending, purification, or labor) should be increased from current levels. If you recommend an increase, specify at most how much the company should be willing to pay for an additional hour of that resource and justify your recommendation.