Problem 1 -
In 2009, the New York Yankees won 103 baseball games during the regular season. The table on the next page lists the number of victories (WIN), the earned -run-average (ERA), and the battling average (AVG) of each team in the American League. The ERA is one measure of the effectiveness of the pitching staff, and a lower number is better. The batting average is one measure of effectiveness of the hitters, and a higher number is better.
TEAM WIN ERA AVG
New York Yankees 103 4.26 0.283
Los Angeles Angels 97 4.45 0.285
Boston Red Sox 95 4.35 0.270
Minnesota Twins 87 4.50 0.274
Texas Rangers 87 4.38 0.260
Detroit Tigers 86 4.29 0.260
Seattle Mariners 85 3.87 0.258
Tampa Bay Rays 84 4.33 0.263
Chicago White Sox 79 4.14 0.258
Toronto Blue Jays 75 4.47 0.266
Oakland Athletics 75 4.26 0.262
Cleveland Indians 65 5.06 0.264
Kansas City Royals 65 4.83 0.259
Baltimore Orioles 64 5.15 0.268
A) Examine the graphs of the data in the accompanying Excel file on the sheet labeled "Regression." Provide a short assessment of the message that the graphs impart. Feel free to make any changes to the graphs to help with your assessment. An example of an assessment (not necessarily true) is "both independent variables (i.e., the x's) show a strong positive relationship with the dependent variable (the y-variable)."
B) After you run the regression analysis, which is the best model for predicting a team's expected wins? Write the equation of the model and interpret the regression coefficients. For example, what happens to wins for a one-unit change in ERA or AVG? What does "a unit change" mean for any variable?
NOTE: Make sure you identify any important results from the regression output in your assessments.
Problem 2-
Emergency calls to Winter Park, Florida's 911 system, for the past 24 weeks are as follows:
WEEK CALLS
1 50
2 35
3 25
4 40
5 45
6 35
7 20
8 30
9 35
10 20
11 15
12 40
13 55
14 35
15 25
16 55
17 55
18 40
19 35
20 60
21 75
22 50
23 40
24 65
A) Examine the graph of the data in the accompanying Excel file on the sheet labeled "Time Series." Provide a short assessment of the message that the graph imparts. Feel free to make any changes to the graph to help with your assessment. An example of an assessment (not necessarily true) is "the data display random noise with no visible trend."
B) Please examine a 2-period and 3-period moving average to forecast for the data. Then do a trend analysis on the data for its forecasting ability. Which of those 3 techniques perform best and by what measure or measures?
Problem 3-
Morgan Arthur has spent the past few weeks determining inventory costs for Armstrong, a toy manufacturer located near Cincinnati, Ohio. She knows that annual demand will be 30,000 units per year and that carrying cost will be $1.50 per unit per year. Ordering cost, on the other hand, can vary from $45 per order to $50 per order. During the past 450 working days, Morgan has observed the following frequency distribution for the ordering cost:
ORDERING COST FREQUENCY
$45 85
$46 95
$47 90
$48 80
$49 55
$50 45
Morgan's boss would like Morgan to determine an EOQ value for each possible ordering cost and to determine an EOQ value for the expected ordering cost.
A) No Excel sheet is provided for this problem. What is the smallest and largest EOQ value for the range of ordering costs? Also, calculate the average ordering cost (not done by just adding up the cost and dividing by 6) and then calculate the EOQ for that value and identify it.
Problem 4-
Finn simply does not have time to analyze all the items in his company's inventory. As a young manager, he has more important things to do. The following is a table of six items in inventory, along with the unit cost and the demand, in units:
IDENTIFICATION CODE UNIT COST DEMAND (Units)
U1 $ 2.00 1,110
V2 $ 5.40 1,110
W3 $ 2.08 961
X4 $ 74.54 1,104
Y5 $ 5.84 1,200
Z6 $ 1.12 896
Which item(s) should be carefully controlled using a quantitative inventory technique, and what item(s) should not be closely controlled?
A) This problem has no Excel sheet, as it is not needed. This problem is to be answered subjectively and not formulaically. As you can see, there is no inventory cost data, so what do you recommend to help Finn determine which items to focus on to determine the optimal EOQ to minimize cost.
Problem 5-
A certification program consists of a series of activities that must be accomplished in a certain order. The activities, their immediate predecessors, and estimated duration appear in the following table:
ACTIVITY IMMEDIATE PREDECESSORS TIME (Days)
a m b
A - 0 2 4
B - 4 5 6
C - 1 1 1
D B 7 10 13
E A, D 3 3 3
F C 2 6 10
G E, F 7 8 9
A) The following shapes represent a portion of the PERT chart that can be constructed for the given data. Complete the depiction by connecting the shapes to show all the possible paths from start to finish for the problem:
B) Identify all the paths and their expected completion times. Of them all, which is the longest and what is its expected completion time?
Problem 6-
The Hardrock Concrete Company has plants in three locations and is currently working on three major construction projects, each located at a different site. The shipping cost per truckload of concrete, daily plant capacities, and daily project requirements are provided in the table below:
FROM/TO | PROJECT A PROJECT B PROJECT C CAPACITIES
PLANT 1 | $10 $ 4 $11 70
PLANT 2 | $12 $ 5 $ 8 50
PLANT 3 | $ 9 $ 7 $ 6 30
PROJECT
RE'QMENTS 40 50 60 150
A) The LP formulation and output results are provided within the accompanying Excel file in sheets labeled "LP" and "Sensitivity Report.." Succinctly answer the following questions:
1) In the solution, Plant 1 is shown not shipping anything to Project C. Why is that? What would happen if shipment were forced to happen from Plant 1 to Project C? (Feel free to cite the results provided to support your points).
2) Is there any way to ascertain whether there are multiple optimal solutions? If so, what is it and are there more than one possible solution for the variables?
3) Identify the preferred item within a pair of options and say why:
a) Pair 1: Increase Plant 1 capacity by 2 or increase Plant 3 capacity by 1, or neither
b) Pair 2: Decrease the truckloads for Project B by 3 or Project C by 2, or neither
c) Pair 3: Increase Plant 2 capacity by 3 or decrease Plant 1 capacity by 2, or neither
d) Pair 4: Increase all 3 Plant capacities by 1 or decrease all Project truckloads by 1, or neither.
Attachment:- Final Exam Sheet.rar