Set 9

The next two questions are based on the following information.

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 (5 points)

Question 1 options:Jane has to sellphotos per week to break even. (Please only enter an integer and include no units.)

Question 2 (5 points)

Question 2 options:If Jane sells 10 units, her profits would bedollars. (Please only enter an integer and include no units.)

Part 2

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 3 (5 points)

If you were to choose the investment that maximizes Paul’s Expected Money Value (EMV), then you should choose __________.Question 3 options:Investment 1Investment 2Indifferent

Question 4 (5 points)

Question 4 options:If Paul is uncertain about the return for Investment 1 in Scenario 1, then this return has to bedollars 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 3

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.

WeekDemandWeek 111Week 214Week 316Week 410Week 515Week 617Week 711Week 814Week 917Week 1012Week 1114Week 1216Week 1315

Question 5 (5 points)

Question 5 options:Using a three week moving average, Sam’s forecast for his Week 14 order number is. (Please round to two decimal points and include no units.)

Question 6 (5 points)

Question 6 options: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. (Please round to two decimal points and include no units.)

Question 7 (5 points)

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?
Question 7 options:Moving averageWeighted moving averageThe sameNot enough information to evaluate.

Part 4

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 is 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 8 (5 points)

Question 8 options:The optimal order quantity is aboutcartons of milk, and the average inventory is aboutcartons. (Please round to the closest integer and include no units.)

Question 9 (5 points)

Question 9 options:Given the optimal order quantity calculated above, if the average inventory is 136 cartons, then the monthly holding cost isdollars, and the total cost including the cost of supply or the total unit cost for all units, holding and ordering isdollars. (Please round to two decimal points and include no units.)

Question 10 (3 points)

Question 10 options:The reorder point iscartons. (Please only enter an integer and include no units.)

Part 5

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 11 (5 points)

Question 11 options:To minimize the cost, the cafeteria should useounces of beef andounces of bread to make the new burger. (Please round to two decimal points and include no units.)

Question 12 (5 points)

Question 12 options: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) isdollars, (Please round to two decimal points and include no units.) and the content of Vitamin A iswhile that for Vitamin B is. (Please round to the closest integer and include no units for the last two answers.)

Part 6

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 TYPEINGREDIENT A (%)INGREDIENT B (%)COST/BARREL ($)X100355530.00X220602534.80

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.

Hint: You may refer to the Low Knock Oil Company example analyzed on page 326-327 in the textbook (Program 8.9), and simply adjust your constraints for the demands accordingly.

Question 13 (3 points)

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?Question 13 options:Yes, yesYes, noNo, yesNo, no

Question 14 (3 points)

Question 14 options:To minimize the production cost, the optimal amount of X100 crude oil used in producing regular gasoline isbarrels, and the optimal amount of X220 crude oil used in producing regular gasoline isbarrel. (Please round to the closest integer and include no units.)

Question 15 (3 points)

Question 15 options:To minimize the production cost, the optimal amount of X100 crude oil used in producing economy gasoline isbarrels, and the optimal amount of X220 crude oil used in producing economy gasoline isbarrel. (Please round to the closest integer and include no units.)

Part 7

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 16 (5 points)

Question 16 options:The average time a car spent in the waiting line ishours, and the total time a car spent in this car wash station ishour. (Please round to two decimal points and include no units.)

Question 17 (3 points)

Question 17 options:The average number of cars in this car wash station is. (Please round to the closest integer and include no units.)

Question 18 (5 points)

Question 18 options:The probability that there are no cars in this station is. (Please round to one decimal points and include no units.)

Question 19 (5 points)

Question 19 options:The probability that there are exactly two cars in this station is. (Please round to three decimal points and include no units.)

Part 8

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.

MeanRangeSample 1471.1Sample 2461.31Sample 3460.91Sample 4471.1Sample 5481.21Sample 6500.82Sample 7490.86Sample 8491.11Sample 9511.12Sample 10520.99Sample 11500.86Sample 12511.2

Question 20 (5 points)

Question 20 options:The overall average weight of a bag of fertilizer ispound, and the average range ispound. (Please round to two decimal points and include no units.)

Question 21 (5 points)

Question 21 options:The upper control limit for a 99.7% control chart for the mean ispound, and the lower control limit ispound. (Please round to two decimal points and include no units. Please enter the upper limit first.)

Question 22 (5 points)

Question 22 options:The upper control limit for a 99.7% control chart for the range ispound, and the lower control limit ispound. (Please round to two decimal points and include no units. Please enter the upper limit first.)