Production / Operations Management
Instructions:
1) Submission: This assignment must be submitted electronically using blackboard assignment manager. Email and physical submissions will not be graded.
2) Submission attempts: You are allowed two attempt for this submission. In each of those attempt, you can upload multiple files. Only the files in the last attempt will be graded. Accordingly, you may not split files across attempts.
3) Due Date: This assignment is due on Monday June 13th by 11:59PM.
4) Late submission: If you do not submit this assignment by the deadline, you may submit it within 48 hours of the deadline. You will receive 20% deduction for late submission. Any later submission will not be graded.
5) Points: This assignment includes 100 points.
6) Questions: This assignment includes 4 questions.
a. Question 1 is Product Mix Problem
b. Question 2 is Transportation Problem
c. Question 3 is Blend Problem
d. Question 4 is Sensitivity analysis
7) Computer Solution: Your computer solution submission must follow the format as specified in lectures and in the BeaverExample.xls.
8) Submission: For this assignment, you need to submit the following:
1. A word file containing the model formulation for each question. (Also containing your answer to (c),(d),(e) of question 4)
2. An Excel file including the Values and Formulas in two separate sheets. As there are 4 questions, you need 8 sheets in an Excel workbook. (For example, sheet 1 is Values of Question 1, sheet 2 is Formulas of Question1, sheet 3 is Values of Question 2, and so on.)
3. Please add your name and section number in the heading of the
Excel sheets and the word file.
Question 1. Product Mix Problem
Lakeside Boatworks is planning to manufacture three types of molded fiberglass recreational boats: a fishing (bass) boat, a ski boat, and a small speedboat. The estimated selling price and variable cost for each type of boat are summarized in the following table:
The company has incurred fixed costs of $2,800,000 to set up its manufacturing operations and begin production. Lakeside has also entered
into agreements with several boat dealers in the region to provide a minimum of 70 bass boats, 50 ski boats, and 50 speedboats. Alternatively, the company is unsure of what the actual demand will be, so it has decided to limit production to no more than 120 of any one boat. The company wants to determine the number of boats that it must sell to break even while minimizing its total variable cost.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the Excel Solver.
Question 2. Transportation Problem
The Cabin Creek Coak (CCC) Company operates three mines in Kentucky and West Virginia, and it supplies coal to four utility power plants along the East Coast. The cost of shipping coal from each mine to each plant, the capacity at each of the three mines, and the demand at each plant are shown in the following table:
The cost of mining and processing coal is $62 per ton at mine 1, $67 per ton at mine 2, and $75 per ton at mine 3. The percentage of ash and sufhur content per ton of coal at each mine is as follows:
Mine %Ash %Sulfur
1 9 6
2 5 4
3 4 3
Each plant has different cleaning equipment. Plant 1 requires that the coalit receives have no more than 6% ash and 5% sulfur; plant 2 coal can have no more than 5% ash and sulfur combines; and plant 3 can have no more than 5% ash and 7% sulfur; and plant 4 can have no more than 6% ash and sulfur combined. CCC wants to determine the amount of coal to produce at each mine and ship to its customers that will minimize its total cost.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the Excel Solver.
Question 3. Blend Problem
A refinery blends four petroleum components into three grades of gasoline- regular, premium, and super. The maximum quantities available of each component and the cost per barrel are as follows:
Component Maximum Barrels
Available/Day Cost/Barrel
1 5000 9
2 2400 7
3 4000 12
4 1500 6
To ensure that each gasoline grade retains certain essential characteristics, the refinery has put limits on the percentage of the components in each blend. The limits as well as the selling prices for the various grades are as follows:
The refinery wants to produce at least 3000 barrels each of super and premium and 4000 barrels of regular. Management wishes to determine the optimal mix of the four components that will maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the Excel Solver.
Question 4. Sensitivity Analysis
Exeter Mines produces iron ore at four different mines, however, the ores extracted at each mine are different in their iron content. Mine 1 produces magnetite ore, which has a 70% iron content; mine 2 produces limonite ore, which has a 60% iron content; mine 3 produces pyrite ore; which has a 50% iron content; and mine 4 produces taconite ore, which has only a 30 % iron content.
Exeter has three customers that produce steel of three types known as Armco, Best and Corcom. Armco needs 400 tons of pure (100%) iron, Best requires 250 tons of pure iron, and Corcom requires 290 tons. It costs $37 to extract and process 1 ton of magnetite ore at mine 1, $46 to produce 1 ton of limonite ore at mine 2, $50 per ton of pyrite ore at mine 3, and $42 per ton of taconite ore at mine 4. Exeter can extract 350 tons of ore at mine 1; 530 tons at mine 2; 610 tons at mine 3 and 490 tons at mine 4. The company wants to know how much ore to produce at each mine in order to minimize cost and meet its customers' demand for 100% pure iron.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the Excel Solver.
c. Do any of the mines have slack capacity? If yes, which one(s)?
d. If Exeter mines could increase production capacity at any one of its mines, which it should be? Why?
e. If Exeter determined that it could increase production capacity at mine 1 from 350 tons to 500 tons, at an increase in production cost to $43 per ton, should it do so?