Part A. Jane wants to setup a photo shop. The cost to rent an office is $150 per week. The variable cost of making one photo is $20 and she can sell it for $50.
Question 1- Jane has to sell _______ photos per week to break even. (Please only enter an integer and include no units.)
Question 2 - If Jane sells 10 units, her profits would be _______ dollars. (Please only enter an integer and include no units.)
Part B. The next two questions are based on the following information.
Paul wants to choose one of the two investment opportunities over three possible scenarios. Investment 1 will yield a return of $10,000 in Scenario 1, $2,000 in Scenario 2, and a negative return of -$5,000 in Scenario 3. Investment 2 will yield a return of $6,000 in Scenario 1, $4,000 in Scenario 2, and zero in Scenario 3. The probability for Scenario 1 is 0.2, for Scenario 2 is 0.3, and for Scenario 3 is 0.5.
Question 1 - If you were to choose the investment that maximizes Paul's Expected Money Value (EMV), then you should choose __________.
A. Investment 1
B. Investment 2
C. Indifferent
Question 2 - If Paul is uncertain about the return for Investment 1 in Scenario 1, then this return has to be _______ dollars in order to make Paul indifferent between these two investments (i.e. the two investments would have the same EMV.) (Please only enter an integer and include no units.)
Part C. The next three questions are based on the following information.
Sam has a cleaning service. To better allocate his resources, he would like to forecast his weekly orders based on the order number he received in the past 13 weeks as shown in the following table.
|
Week
|
Demand
|
|
Week 1
|
11
|
|
Week 2
|
14
|
|
Week 3
|
16
|
|
Week 4
|
10
|
|
Week 5
|
15
|
|
Week 6
|
17
|
|
Week 7
|
11
|
|
Week 8
|
14
|
|
Week 9
|
17
|
|
Week 10
|
12
|
|
Week 11
|
14
|
|
Week 12
|
16
|
|
Week 13
|
15
|
Question 1 - Using a three week moving average, Sam's forecast for his Week 14 order number is _____.
Question 2 - Using a three week weighted moving average with weights 3, 2, and 1 given to the most recent, second most recent, and third most recent week, respectively, Sam's forecast for his Week 14 order number is ______.
Question 3 - If the MAD for moving average is 4.17 and the MAD for weighted moving average is 2.38, then which forecast is more accurate?
A. Moving average
B. Weighted moving average
C. The same
D. Not enough information to evaluate.
Part D. The next three questions are based on the following information.
A grocery store needs to sell 3,000 cartons of 2L 2% milk per month. The sales are relatively constant throughout the month. The owner of this grocery store purchases milk from a supplier 50 miles away for $2 per carton, and it takes a day to restock. The holding cost per carton per month is $1.5, and the ordering cost per order is about $18.5 including labor, gas and depreciation. Consider a month of 30 days.
Question 1 - The optimal order quantity is about ______ cartons of milk, and the average inventory is about _____ cartons.
Question 2 - Given the optimal order quantity calculated above, if the average inventory is 136 cartons, then the monthly holding cost is _____ dollars, and the total cost including the cost of supply or the total unit cost for all units, holding and ordering is ______ dollars.
Question 3 - The reorder point is ______ cartons.
Part E. The next two questions are based on the following information.
A cafeteria wants to introduce a new burger, with bread and beef together weighing at least 1 ounce. The cafeteria manage also wants the new burger to meet a new nutrition standard, i.e. contains at least 7 units of Vitamin A and 10 units of Vitamin B. Each ounce of beef contains 1 unit Vitamin A and 6 units of Vitamin B, while each ounce of bread contains 2 units Vitamin A and 1 units of Vitamin B. The price of beef is $0.5 per ounce and the price of bread is $0.1 per ounce.
Question 1 - To minimize the cost, the cafeteria should use ____ ounces of beef and _____ ounces of bread to make the new burger.
Question 2 - If the cafeteria uses 1.18 ounces of beef and 2.91 ounces of bread to make the new burger, the total cost of the new burger (excluding other ingredients) is ____ dollars, (Please round to two decimal points and include no units.) and the content of Vitamin A is while that for Vitamin B is ______.
Part F. The next three questions are based on the following information.
The Low Knock Oil Company produces two grades of cut-rate gasoline for industrial distribution. The grades, regular and economy, are produced by refining a blend of two types of crude oil, type X100 and type X220. Each crude oil differs not only in cost per barrel, but in composition as well. The following table indicates the percentage of crucial ingredients found in each of the crude oils and the cost per barrel for each:
|
CRUDE OIL TYPE
|
INGREDIENT A (%)
|
INGREDIENT B (%)
|
COST/BARREL ($)
|
|
X100
|
35
|
55
|
30.00
|
|
X220
|
60
|
25
|
34.80
|
Weekly demand for the regular grade of Low Knock gasoline is at least 25,000 barrels, and demand for the economy is at least 32,000 barrels per week. At least 45% of each barrel of regular must be ingredient A. At most 50% of each barrel of economy should contain ingredient B. While the gasoline yield from one barrel of crude depends on the type of crude and the type of processing used, we will assume for the sake of this example that one barrel of crude oil will yield 0.46 barrel of gasoline.
Question 1 - At the optimal production, does the company just make enough regular gasoline to meet the demand? Does the company just make enough economy gasoline to meet the demand?
A. Yes, yes
B. Yes, no
C. No, yes
D. No, no
Question 2 - To minimize the production cost, the optimal amount of X100 crude oil used in producing regular gasoline is ________ barrels, and the optimal amount of X220 crude oil used in producing regular gasoline is _______ barrel.
Question 3 - To minimize the production cost, the optimal amount of X100 crude oil used in producing economy gasoline is _____ barrels, and the optimal amount of X220 crude oil used in producing economy gasoline is ______ barrel.
Part G. The next four questions are based on the following information. At a car wash station, on average, there are 4 cars coming in for the service every 10 minutes. The average wash time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. Please convert all rates into cars per hour and answer the following questions.
Question 1 - The average time a car spent in the waiting line is _____ hours, and the total time a car spent in this car wash station is ______ hour.
Question 2 - The average number of cars in this car wash station is _______.
Question 3 - The probability that there are no cars in this station is ______.
Question 4 - The probability that there are exactly two cars in this station is _______ .
Part H. The next three questions are based on the following information.
To study the weight accuracy of a 50lb fertilizer bag, 12 samples of 12 bags of fertilizer in each sample were taken and the results are as follows.
|
|
Mean
|
Range
|
|
Sample 1
|
47
|
1.1
|
|
Sample 2
|
46
|
1.31
|
|
Sample 3
|
46
|
0.91
|
|
Sample 4
|
47
|
1.1
|
|
Sample 5
|
48
|
1.21
|
|
Sample 6
|
50
|
0.82
|
|
Sample 7
|
49
|
0.86
|
|
Sample 8
|
49
|
1.11
|
|
Sample 9
|
51
|
1.12
|
|
Sample 10
|
52
|
0.99
|
|
Sample 11
|
50
|
0.86
|
|
Sample 12
|
51
|
1.2
|
Question 1 - The overall average weight of a bag of fertilizer is ____ pound, and the average range is ____ pound.
Question 2 - The upper control limit for a 99.7% control chart for the mean is _____ pound, and the lower control limit is ____ pound.
Question 3 - The upper control limit for a 99.7% control chart for the range is ___ pound, and the lower control limit is _____ pound.