Fundamentals of Analytics and Business Intelligence
Linear Programming (LP) and Sensitivity Analysis
Stop Fast Brakes makes brake disc pads for motor vehicles at three locations: Plant 1-Florida, Plant 2- California, and Plant 3-Texas. The profit contribution for each disc pad at each plant is $300, $280, and $225 respectively. Each plant has sufficient capacity to produce 750 disc pads per week. Stop Fast has 525 workers and each can work up to 40 hours per week. Currently the firm has 9,400 units of raw materials in stock. Every week, at least 1400 disc pads must be produced across all three plants. Labour and raw material requirements at each plant are shown below.
|
PLANT
|
LABOUR (hrs)
|
RAW MATERIAL (units)
|
|
1 (Florida)
|
20
|
5
|
|
2 (California)
|
16
|
8
|
|
3 (Texas)
|
10
|
7
|
Please note: You are required to submit the Microsoft Excel file and Microsoft Word file for this assignment. All workings should be shown and explained and all questions must be numbered appropriately.
1. Formulate a LP model for this problem. 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 make decisions about what to do. The maximum attainable profit is required. Develop a simple DSS prototype to solve this problem.
a. How many disc pads should be produced at each plant?
b. What is the total profit realized?
c. What is the profit contribution for each plant?
For the question 3, make sure to undo each change (put back to original value) after each question is completed.
3. Perform sensitivity analysis to determine:
a. What would happen if 5 more workers are hired? Please explain the total impact of this decision on the production process, and at most how much each of these workers should be paid each week.
a. Due to economic factors, the profit for producing disc pads in California has gone up by $25. Evaluate and discuss the impact of this.
b. The profit for producing disc pads in Texas has gone DOWN to $200 each and the plant capacity increased by 200. Evaluate and discuss the impact of this, and if you would recommend this change
4. Write a short memo to the management of Stop Fast Brakes, explaining:
a. Over what range of raw material units is the dual price applicable, and what does the raw material constraint shadow price value mean?
b. Which plant capacity should the company work to increase and which one/s should not be increased? Explain the reason for your decision