Assignment :
A chemical manufacturing company produces three types of industrial solvents, S1, S2, and S3.
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 175 hours for blending, 305 hours for purification, and 160 labor hours available. The requirements for each solvent are shown in the table below:
S1 S2 S3
Blending (hours/1000gallons) 2 3 2
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 below:
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. The maximum attainable profit is required. Develop a simple DSS prototype to solve this production planning problem.
a. How many gallons of S1, S2, and S3 are produced under this optimal product mix?
b. What is the maximum attainable profit?
c. What is the profit contribution for each solvent (S1, S2, S3)?
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
4. Write a short memo to the vice-president of production and address the following:
a. Interpret the sensitivity and limit reports
b. Make recommendations on 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.