Reference no: EM131168574

This part of the question is based on the following information.

The Schmedley Discount Department Store has approximately 300 customers shopping in its store between 9 A.M. and 5 P.M. on Saturdays. In deciding how many cash registers to keep open each Saturday, Schmedley's manager considers two factors: customer waiting time (and the associated waiting cost) and the service costs of employing additional checkout clerks. Checkout clerks are paid an average of $8 per hour. When only one is on duty, the waiting time per customer is about 10 minutes (or hour); when two clerks are on duty, the average checkout time is 6 minutes per person; 4 minutes when three clerks are working; and 3 minutes when four clerks are on duty.

Schmedley's management has conducted customer satisfaction surveys and has been able to estimate that the store suffers approximately $10 in lost sales and goodwill for every hour of customer time spent waiting in checkout lines.

Please fill out the following table to answer the quiz questions in Part 1. (You may also download the attached worksheet.)

                                                           Number of checkout clerks                        
                                                              1               2           3             4
Number of customers                         300            300     300            300

Average waiting time (per customer)
Total customer waiting time
Cost per waiting hour
Total waiting cost
Checkout clerk hourly salary
Total pay of clerks for an 8-hour shift
Total expected cost

Question 1:

The total customer waiting time is ___ hours when there is only one clerk, and it will be reduced to only ___ hours if there are four clerks. (Please only enter an integer and include no units.)

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Question 2:

The total wait cost is ____  dollars when there is only one clerk, and it will be reduced to only ____ dollars if there are four clerks. (Please only enter an integer and include no units.)

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Question 3:

The total cost of hiring is only ____ dollars when there is only one clerk, and it will be increased to _____ dollars if there are four clerks. (Please only enter an integer and include no units.)

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Question 4:

To minimize the total expected cost based on your calculations above, the optimal number of clerks to have on duty each Sunday is ___.

A.1

B.2

C.3

D.4

Question 5: This part of the question is based on the following information.

The wheat harvesting season in the American Midwest is short, and most farmers deliver their truckloads of wheat to a giant central storage bin within a two-week span. Because of this, wheat-filled trucks waiting to unload and return to the fields have been known to back up for a block at the receiving bin. The central bin is owned cooperatively, and it is to every farmer's benefit to make the unloading/storage process as efficient as possible. The cost of grain deterioration caused by unloading delays, the cost of truck rental, and idle driver time are significant concerns to the cooperative members. Although farmers have difficulty quantifying crop damage, it is easy to assign a waiting and unloading cost for truck and driver of $18 per hour. The storage bin is open and operated 16 hours per day, 7 days per week, during the harvest season and is capable of unloading 35 trucks per hour according to an exponential distribution. Full trucks arrive all day long (during the hours the bin is open) at a rate of about 30 per hour, following a Poisson pattern.

The cooperative, as mentioned, uses the storage bin only two weeks per year. Farmers estimate that enlarging the bin would cut unloading costs by 50% next year. It will cost $9,000 to do so during the off season.

Question 5:

The average number of trucks in the system is ____ trucks. (Please only enter an integer and include no units.)

Question 6:

The average time per truck spent in the system is ______ minutes. (Please only enter an integer and include no units.)

Question 7:

The utilization rate for the bin area is _______ . (Please round it to two decimal points.)

Question 8:

The probability that there are more than 3 trucks in the system is about _____. (Please round it to two decimal points.)

Question 9:

The total daily cost in the unloading process____ is per day. (Please only enter an integer and include no units.)

Question 10:

Based on the above calculation, the net saving/loss of enlarging the bin is ___  dollars, hence the cooperative ____ proceed to enlarge the bin. (Please round to an integer and include no units. Use a "-" sign in front the number to indicate a net loss, if there is a loss. Also, enter only "should" or "should not" in the second blanket.)

When set at the standard position, Autopitch can throw hard balls toward a batter at an average speed of 60 mph. Autopitch devices are made for both major- and minor-league teams to help them improve their batting averages. Autopitch executives take samples of 10 Autopitch devices at a time to monitor these devices and to maintain the highest quality. The average range is 3 mph. Using control chart techniques, determine control-chart limits for averages and ranges for Autopitch.

Please use the attached table or Excel QM to answer the following questions.

Question 1

Based on the attached table or Excel QM, the upper control limit for averages is____. 

Question 2

Based on the attached table or Excel QM, the lower control limit for averages is ___.

Question 3

Based on the attached table or Excel QM, the upper control limit for ranges ____. 

Question 4

Based on the attached table or Excel QM, the lower control limit for ranges is ___. 

This part of the question is based on the following information.

Colonel Electric is a large company that produces light bulbs and other electrical products. One particular light bulb is supposed to have an average life of about 1,000 hours before it burns out. Periodically the company will test 5 of these and measure the average time before these burn out. The attached table gives the results of 10 such samples.

Question 5

The overall average of these means is ___, and the overall average range is ___. 

Question 6

Based on the result in Question 5 and the attached table for Part 1 or Excel QM, the upper control limit for a 99.7% control chart for the mean/average is _____.

Question 7

Based on the result in Question 5 and the attached table in Part 1 or Excel QM, the lower control limit for a 99.7% control chart for the mean/average is ____.

Question 8

Does this process appear to be in control in terms of the mean?

A. Yes.

B. No.

Question 9

Based on the result in Question 5 and the attached table for Part 1 or Excel QM, the upper control limit for a 99.7% control chart for the range is ___ and the thelower control limit is ____ . (Please round it to two decimal points and include no units.)

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Question 10

Does this process appear to be in control in terms of the range?

A.Yes.

B.No.

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The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for a $15 profit.

Now, Electrocomp's management also realizes that there should be a minimum number of air conditioners produced in order to fulfill a contract. Also, due to an oversupply of fans in the preceding period, a limit should be placed on the total number of fans produced.

Question 1

If Electrocomp decides that at least 20 air conditioners should be produced but no more than 80 fans should be produced, the optimal production mix of air conditioners and fans is __________. (The first number is for air conditioners and the second for fans.)

A.(50,30)

B.(20,80)

C.(40,60)

D.(26.67,80)

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Question 2

In the optimal solution for the above question (Question 1), the slack for the four constrains - Total hours of wiring, Total hours of drilling, Number of air conditioners, Number of fans are __________, respectively. (Hint: A negative number shows that the constraint is binding downward, i.e. it sets a lower rather than an upper limit. You may take the negative sign out when interpreting the results.)

A.0, 0, 20, 20
B.0, 0, 10, 20

C.0, 0, 20, 10

D.10, 10, 10, 10
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Question 3

If Electrocomp decides that at least 30 air conditioners should be produced but no more than 50 fans should be produced, the optimal production of air conditioners is _____ and the optimal production of fans is ______. (Please only enter an integer and include no units.)

Question 4

In the optimal solution for the above question (Question 3), the slack for the four constrains - Total hours of wiring, Total hours of drilling, Number of air conditioners, Number of fans are __________, respectively. (Hint: A negative number shows that the constraint is binding downward, i.e. it sets a lower rather than an upper limit. You may take the negative sign out when interpreting the results.)

A.0, 0, 15, 10
B.5, 0, 15, 0

C.0, 5, 15, 0

D.0, 0, 10, 15
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Part 2

The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 feet of good-quality redwood. Each bench that Outdoor Furniture produces requires 4 labor hours and 10 feet of redwood; each picnic table takes 6 labor hours and 35 feet of redwood. Completed benches will yield a profit of $9 each, and tables will result in a profit of $20 each.

Question 5

The optimal production of benches is _____ and the optimal production of tables is _____. (Please only enter an integer and include no units. Hint: Because of the resource constraints, you may not be able to produce 4 tables even if the solution is 3.8; you may have to just produce 3 tables.)

Part 3

A winner of the Texas Lotto has decided to invest $50,000 per year in the stock market. Under consideration are stocks for a petrochemical firm and a public utility. Although a long-range goal is to get the highest possible return, some consideration is given to the risk involved with the stocks. A risk index on a scale of 1-10 (with 10 being the most risky) is assigned to each of the two stocks. The total risk of the portfolio is found by multiplying the risk of each stock by the dollars invested in that stock. The attached table provides a summary of the return and risk. The investor would like to maximize the return on the investment, but the average risk index of the investment should not be higher than 6.

Question 6

The optimal dollar amount invested in Petrochemical stock is _________ dollars, and the optimal dollar amount invested in Utility stock is ___________ dollars. (Please only enter an integer and include no units. Hint: The total risk on each stock is the risk index times the investment in dollars. When you use Excel QM, you need to end the total risk in the right hand side of the constraint not simply the risk index.)

A.20,000, 30,000

B.30,000, 20,000

C.10,000, 15,000

D.15,000, 10,000

Question 7

The average risk index (not in dollar amount) for the optimal investment is ____ , and the estimated best/maximum return for this investment is ______. (Please only enter an integer and include no units.)

Part 4

This part of the question is based on the following information.

The Heinlein and Krampf Brokerage firm has just been instructed by one of its clients to invest $250,000 of her money obtained recently through the sale of land holdings in Ohio. The client has a good deal of trust in the investment house, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm select whatever stocks and bonds they believe are well rated, but within the following guidelines:

(a) Municipal bonds should constitute at least 20% of the investment.
(b) At least 40% of the funds should be placed in a combination of electronic firms, aerospace firms, and drug manufacturers.
(c) No more than 50% of the amount invested in municipal bonds should be placed in a high-risk, high-yield nursing home stock.
Subject to these restraints, the client's goal is to maximize projected return on investments. The analysts at Heinlein and Krampf, aware of these guidelines, prepare the attached list of high-quality stocks and bonds and their corresponding rates of return.

Hint: You will need to rearrange one of the constraints in this problem so that all variables will be at the left hand side of the constraint and the right hand side of the constraint will be zero. You may adjust he sign of the constraint accordingly. For example, rearranging x < y + 2 to x - y < 2.

Question 8

The optimal money invested in the five stocks and bonds - Municipal bonds, Electronics, Aerospace, Drugs, and Nursing homes are __________ dollars, respectively.

A.50,000, 50,000, 50,000, 50,000, 50,000
B.50,000, 0, 0, 175,000, 25,000

C.25,000, 0, 0, 175,000, 50,000

D.50,000, 25,000, 25,000, 125,000, 25,000

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Part 5

Mt. Sinai Hospital in New Orleans is a large, private, 600-bed facility, complete with laboratories, operating rooms, and x-ray equipment. In seeking to increase revenues, Mt. Sinai's administration has decided to make a 90-bed addition on a portion of adjacent land currently used for staff parking. The administrators feel that the labs, operating rooms, and x-ray department are not being fully utilized at present and do not need to be expanded to handle additional patients. The addition of 90 beds, however, involves deciding how many beds should be allocated to the medical staff for medical patients and how many to the surgical staff for surgical patients.

The hospital's accounting and medical records departments have provided the following pertinent information. The average hospital stay for a medical patient is 8 days, and the average medical patient generates $2,280 in revenues. The average surgical patient is in the hospital 5 days and receives a $1,515 bill. The laboratory is capable of handling 15,000 tests per year more than it was handling. The average medical patient requires 3.1 lab tests and the average surgical patient takes 2.6 lab tests. Furthermore, the average medical patient uses one x-ray, whereas the average surgical patient requires two x-rays. If the hospital was expanded by 90 beds, the x-ray department could handle up to 7,000 x-rays without significant additional cost. Finally, the administration estimates that up to 2,800 additional operations could be performed in existing operating room facilities. Medical patients, of course, do not require surgery, whereas each surgical patient generally has one surgery performed.

Assume that the hospital is open 365 days a year. Round off your answers to the nearest integer.

Question 9

The optimal number of medical patients per year is ____, and optimal number of surgical patients per year is ____. The maximum annual profit is ____dollars.

Question 10

Among the 90 additional beds, _______ beds should be used for medical patients and _______ beds used for surgical patients.

A.45, 45

B.60, 30
C.61, 29

D.29, 61

Question 11

At the optimal, there are empty beds, lab tests of unused capacity, x-rays of unused capacity, and unused operation rooms available. (Please round to the closest integer and include no units.)

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