Exercise 1 Forecasting
Using the data below, complete the following questions by hand (note: I want to see all of your work):
Period 
Month 
Actual Issues Remediated 
1 
March 
355 
2 
April 
234 
3 
May 
267 
4 
June 
189 
5 
July 
301 
6 
August 
222 
7 
September 
245 
8 
October 
432 
9 
November 
324 
10 
December 
187 
 Use a 3month moving average model to forecast issues remediated for periods 610. (15 points)
 Use a 5month moving average model to forecast issues remediated for periods 610. (15 points)
 Use an exponential smoothing model with a =.2 to forecast issues remediated for periods 610. (Assume a beginning forecast of 320 for period 5). (15 points)
 Use an exponential smoothing model with a =.4 to forecast issues remediated for periods 610. (Assume a beginning forecast of 320 for period 5) (15 points)
 Compare the forecasts in questions 1 through 4. Which is best? Why? Support your answer. (20 points)
 Starting with your solution to question 4, complete a double smoothing model for periods 610 for issues remediated. Again here, assume a beginning forecast of 320 for period 5. How does this model perform compared to question 4? Support you answer with statistics. (20 points)
Study Guide Exam 1
Review the Introduction chapter there will be a few questions on the basic information
Forecasting Chapter 3
 Forecasting Definition
 Smoothing Constant Low Alpha vs High Alpha
 Minimizing error
 Reactions to changes
 Forecasting Method Techniques
 Weighted average moving forecast
 How to work through this type of forecast like the quiz
 Moving Average Forecast
 How to work through this type of forecast
 What is needed for this forecast
 Smoothing Forecast
 How to work through this type of forecast
 Double Smoothing Forecast
 How to work through this type of forecast
 Tracking Signal Definition
 MAD
 definition
 How to calculate this
 BIAS
 definition
 How to calculate this
Capacity Chapter 5
 Capacity Definition
 Key capacity planning questions
 Related capacity planning questions
 Effective Capacity
 Definition
 How to work through the equation
 Design Capacity
 Definition
 How to work through the equation
 Capacity strategy
 Actual Output definition
 Inputs vs outputs
 Examples of what these are
 Efficiency Equations
 Work through the examples from the slides
 Utilization Equations
 Work through the examples from the slides
 Capacity Cushion Equations
 Profit Equations
 Work through all of the examples from the slides
 Breakeven Equations
 Work through all of the examples from the slides
 Feasible solution space definition
Linear Programming Chapter 19
 Linear Programming Definition
 Steps to setting the problem up
 Constraints
 How to find these in a word problem
 Feasible solution definition
 Objective Functions
 The format of how this is written
 How to find these in a word problem
 Right Hand Side information from slides
 Sensitivity Analysis
 What’s included in this? From slides in class
 Binding Constraints definition vs nonbinding constraint definition
 Redundant Constraint definition
 Non Negativity Constraint
 How to find these in a word problem
Exercise 2 Linear Programming
 Answer the below problem using LINDO. Show all of your work where it is possible.
Banana Boat produces two similar products, Sun Block SPF 30 and Tanning Oil SPF 8. Sun Block is made of 40 pounds or raw material A and 60 pounds of raw material B, while Tanning Oil is made of 50 pounds of material A and 30 pounds of material B. For this production period, the company has a supply of only 75,000 pounds of material A and 88,000 pounds of material B. Based on demand, Banana Boat needs to sell at least 1200 Sun Blocks and 500 Tanning Oils each month. The profit contributions are $10 and $7 per product, respectively, for Sun Block and Tanning Oil. What is the number of each product to be produced to maximize total profit?
 Describe the Decision Variables (5 points)
 Describe the Objective Function (5 points)
 List all of the Constraints (15 points)
 Attach the LINDO Solution and describe the optimal solution. (15 points)
 Answer the below problem using LINDO. Show all of your work where it is possible.
Yeti produces three products, Coolers, Water Bottles, and Dog Bowls. Coolers are made of 4 hours of Machine A and 3 hours of machine B. Water Bottles are made of 1 hour of Machine A, 2 hours of Machine B, and 1.5 hours of Machine C. Dog Bowls are made of 1.5 hours of machine B and 2.5 hours of machine C. For this production period, the company has a supply of only 260 hours for Machine A, 230 hours of Machine B, and 75 hours of Machine C. Based on demand, Yetti needs to sell at least 35 Coolers and 20 Water Bottles each month. The profit contributions are $40, $22, and $13 per product, respectively, for Coolers, Water Bottles, and Dog Bowls. What is the number of each product to be produced to maximize total profit?
 Describe the Decision Variables (5 points)
 Describe the Objective Function (5 points)
 List all of the Constraints (15 points)
 Attach the LINDO Output and describe the optimal solution. (15 points)
 What would it take to produce Dog Bowls? Explain how you found your solution. (5 points)
 The below output came from the optimal solution of a toy manufacturing company. The printer had problems and wasn’t able to appropriately fill out the LINDO output. Without using LINDO/LINO, please fill in the blank answers and explain how you got to your answer. (15 Points)
INPUT:
OUTPUT:
BUAD306
Grasso
Exercise 5 PERT/CPM
Grasso Construction Company
In 2018, Grasso Construction Company had received a contract to construct a water purification system for the city of Wilmington. By the fall of 2019, work was nearly complete on the main system; however, it was apparent that work on a special remote control building would have to be finished earlier than originally planned if the main system was to be completed on time.
Mr. Jason Barnes, field construction supervisor for Grasso Construction Company had arranged a meeting with Ms. Addison Lee, project engineer, to restudy the arrow diagram of their critical path schedule for the construction of the remotecontrol building in an effort to determine the shortest possible time in which the job could be done without spending more money than necessary.
Grasso Construction used the Critical Path Method as a tool to assist in project planning and control. A list of the activities for the remotecontrol site is in Exhibit 1. The Cost Table, Exhibit 2, lists the activities and their duration along with the cost needed to complete them in this “normal time”. The Cost Table also lists the minimum amount of time that each activity will require, called the “crash” time. In addition, a final listing in the Cost Table shows how much it will cost to shorten each activity by one week. The sequence of consecutive activities requiring the longest time to complete before the end of the project is known as the “critical path” for that project. The path is considered “critical” because any delay in the particular sequence will delay the completion of the entire project.
Exhibit 1
Job Label 
Job Description 
Immediately Preceding Job 
Normal Time t_{e} 
t_{p} 
A 
Procure materials 
Start 
3 
4 
B 
Prepare site 
Start 
6 
8 
C 
Prepare request for Wilmington Engineering department approval 
Start 
2 5 
3 
D 
Prefabricate building and deliver to site 
A 
5 
7 
E 
Obtain Wilmington Engineering department approval 
C 
2 
3 
F 
Install connecting lines to main system 
A 
7 
8 
G 
Erect building and equipment on site 
B, D, E 
4 
6 
Exhibit 2
Cost Table for Remote Control Building Project

Normal 
Crash 
Activity 
t_{e} (Weeks) 
Dollars 
t_{o} (Weeks) * 
Dollars** 
A 
3 
$ 5,000 
2 
$ 5,000 
B 
6 
$ 14,000 
4 
$ 6,000 
C 
2 
$ 2,500 
1 
$ 2,500 
D 
5 
$ 10,000 
3 
$ 4,000 
E 
2 
$ 8,000 
2 
– 
F 
7 
$ 11,500 
5 
$ 3,000 
G 
4 
$ 10,000 
2 
$ 7,000 
Total Project Cost
(No Crashing) 
$ 61,000 


*Crash weeks shown represent the minimum possible time for the given activity, t_{o}.
**This is the cost of gaining one week over the normal time by use of “crash” methods.
Answer the following questions regarding Grasso Construction Company. Be sure to answer every single question in each individual part.:
 (25 points) Draw a PERT/CPM diagram of this building project. I need to see your drawing.
 What is the critical path?
 How long will it take to complete the project without crashing?
 What is the associated cost?
 Revise the schedule in order to complete the job within 10 weeks using the crashing method. Indicate the new cost and critical path or paths.
 (25 points) Starting from the original tables listed in the exhibits above, Grasso Construction will need to use a new 10week schedule. However, it became obvious that it would take not two but five weeks to prepare the necessary data for Activity C and that this step alone would now cost $7,000.
 What steps would you take to keep on schedule?
 What would be your new critical path or paths?
 What would happen to project costs? (Assume that activity C cannot be crashed.)
 (25 points) Assume that the project was planned for completion in six weeks and that activity C, the preparation for approval, would take two weeks as described in the case (i.e., go back to where you left off at the end of part 1).
 If there is a penalty cost of $10,000 per week for every week the project is late, what action would you take?
 Can you expedite the project so as to finish in 6 weeks?
 (25 points) What is the probability of completing this building project in 9 weeks?
BUAD306
Grasso
Exercise 2 Linear Programming
 Answer the below problem using LINDO. Show all of your work where it is possible.
Banana Boat produces two similar products, Sun Block SPF 30 and Tanning Oil SPF 8. Sun Block is made of 40 pounds or raw material A and 60 pounds of raw material B, while Tanning Oil is made of 50 pounds of material A and 30 pounds of material B. For this production period, the company has a supply of only 75,000 pounds of material A and 88,000 pounds of material B. Based on demand, Banana Boat needs to sell at least 1200 Sun Blocks and 500 Tanning Oils each month. The profit contributions are $10 and $7 per product, respectively, for Sun Block and Tanning Oil. What is the number of each product to be produced to maximize total profit?
 Describe the Decision Variables (5 points)
 X1= # of sun blocks
 X2= # of tanning oil
 Describe the Objective Function (5 points)
 List all of the Constraints (15 points)
 Raw material A 40×1+ 50X2 <= 75000
 Raw material B 60×1+ 30×2 <= 88000
 Demand Sunblock x1>= 1200
 Demand Tanning Oil x2>= 500
 Attach the LINDO Solution and describe the optimal solution. (15 points)
 Answer the below problem using LINDO. Show all of your work where it is possible.
Yeti produces three products, Coolers, Water Bottles, and Dog Bowls. Coolers are made of 4 hours of Machine A and 3 hours of machine B. Water Bottles are made of 1 hour of Machine A, 2 hours of Machine B, and 1.5 hours of Machine C. Dog Bowls are made of 1.5 hours of machine B and 2.5 hours of machine C. For this production period, the company has a supply of only 260 hours for Machine A, 230 hours of Machine B, and 75 hours of Machine C. Based on demand, Yeti needs to sell at least 35 Coolers and 20 Water Bottles each month. The profit contributions are $40, $22, and $13 per product, respectively, for Coolers, Water Bottles, and Dog Bowls. What is the number of each product to be produced to maximize total profit?
 Describe the Decision Variables (5 points)
 X1= Coolers
 X2= Water Bottles
 X3= Dog Bowls
 Describe the Objective Function (5 points)
 List all of the Constraints (15 points)
 Machine A 4X1+ 1X2 <= 260
 Machine B 3X1 + 2X2 + 1.5X3 <= 230
 Machine C 5X2+ 2.5X3 <=75
 Demand Coolers X1 >= 35
 Demand Water Bottles X2 >=20
 NonNegativity Dog Bowls X3 >=0
 Attach the LINDO Output and describe the optimal solution. (15 points)
 What would it take to produce Dog Bowls? Explain how you found your solution. (5 points)
The price would need to go up by 1.4 (reduced cost) since that is the improvement needed in the coefficient for a current zero variable to become positive
 The below output came from the optimal solution of a toy manufacturing company. The printer had problems and wasn’t able to appropriately fill out the LINDO output. Please fill in the blank answers and explain how you got to your answer. (15 Points)
INPUT:
OUTPUT:
 By using the values and plugging them into the objective function, you would get the following input: 3(8)+7(5)+4(13)= 111.00
 Since the slack or surplus value has a number other than 0, your dual price would be 0.00
 By looking at the original objective function equation, you would see that the current coefficient is 4.00
Exercise 3 Location Planning and Analysis
A firm has four manufacturing plants and four warehouses. It is trying to determine the optimal way to ship from its plants to the warehouses.
The plant capacities and warehouse requirements are as follows:
Plant Capacity Warehouse requirement
1 = 1200 A = 3100
2 = 4200 B = 1800
3 = 5000 C = 2000
4 = 2000 D = 4400
The freight charges per unit from each plant to each warehouse are as follows:
Plant 
Warehouse 
A 
B 
C 
D 
1
2
3
4 
$9
$6
$8
$7 
$5
$8
$9
$9 
$6
$11
$9
$8 
$7
$6
$5
$8 
 Find an initial feasible solution using Northwest Corner and find the cost of this solution. Set this up with Warehouse going across the columns at the top and Plants going down the rows as it is shown in the picture above. (18 Points)
 Find an initial feasible solution using the NorthSouth rule and find the cost of this solution. Set this up with Warehouse going across the columns at the top and Plants going down the rows as it is shown in the picture above. (18 Points)
 Find an initial feasible solution using the Difference method and find the cost of this solution. Set this up with Warehouse going across the columns at the top and Plants going down the rows as it is shown in the picture above. (18 Points)
 Formulate this problem as a transportation Linear Programming problem using LINDO. Show me the decision variables, objective function, constraints and the LINDO output. Find the cost of this solution and describe the optimal solution. (26 Points)
 How does the Linear Programming solution compare to the solutions found in questions 13? Describe the different outcomes. (20 Points)
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