A.Executives of a large discount drug store are concerned with customers balking from the single check-out lines in their stores because they are wa

A.Executives of a large discount drug store are concerned with customers balking from the single check-out lines in their stores because they are waiting too long. The executives have set the objective of increasing sales by improving customer check-out service. For that purpose, they have hired a data analytics consultant.

The consultant has studied the operations of a particular store and has learned the following information. Customers get on the single check-out line in the stores at the mean rate of 28 per hour. Once on the line, customers are then served on a first-come, first-served, basis. On average, one cashier, working alone, can check-out a customer in two minutes. Working together as a team, an additional cashier reduces the check-out time of a customer by 15 seconds, on average. The manager has also discovered that, on average, customers will balk if their wait on the line is five minutes or more. (Assume Poisson arrivals and exponential service times.)

NOTES:

In this problem, report all probabilities rounded to four decimal places and report all times as minutes and decimal seconds.

In part 12 you MUST provide a copy of your Excel spreadsheet containing your calculations for problem A to receive credit for this problem. You are also reminded to submit all of your computer files for this problem with your completed exam to the Final Exam link on Bb. Failure to provide either of these deliverables will result in this problem NOT being scored.

1.In new lines entered below this part, describe the state and/or situation of the waiting line if only a single cashier is working the check-out counter. Specifically, is this a viable system?2.a.In new lines entered below this part, state the appropriate operating characteristic used as the criterion for this problem.

b.In new lines entered below this part, state algebraically the specific criterion the consultant is using in terms of the operating characteristic stated in part a.

3.In new lines entered below this part, state the minimum total number of cashiers needed to meet the consultants objective.

For the minimum number of cashiers stated in part 3 above, enter your responses for items 4 through 11 below.

4.In new lines entered below this part, state the probability that the check-out line is empty of customers.

5.In new lines entered below this part, state how long, reported in minutes and seconds, is the mean time that customers are expected to have to wait on the check-out line.

6.In new lines entered below this part, on average, state how many customers are expected to be waiting on the line.

7. In new lines entered below this part, state how long, reported in minutes and seconds, is the mean time for a cashier to check-out a customer.

8.In new lines entered below this part, state the chance that a customer will have to wait on the line before being served by a cashier.

9.In new lines entered below this part, state the chance that a customer will be taken by the cashier right away without having to wait at all.

10.In new lines entered below this part, state how much time it will take on average for customers to check-out, from the time they arrive on the waiting line until the time they leave the cashier. Report the time in minutes and seconds.11.In new lines entered below this part, state the chance that the check-out line is empty for five minutes so that all the cashiers can take a short break for personal business without being interrupted by the arrival of a customer. (Simply put, state the chance that no customers will arrive in a five-minute period.)

12.In a space created below this part, you must present HERE a copy of your Excel spreadsheet for problem A.

AND submit all of your computer files for this problem with your completed exam to the Final Exam link on Bb. Include in the filename/tab name Prob A.

B.The XYZ Foods Company has developed a new sport beverage that it intends to advertise during the Super Bowl. XYZs advertising company can purchase one, two, or three 30-second TV commercials advertising the drink.

Analysts at XYZs ad agency have developed the table below containing the net profits resulting from purchasing one, two, or three advertising spots given the level of fan excitement in the game. (Values are in $1,000,000 [$1M]; negative values denote losses.) Another possibility (not listed) is that XYZ may opt to not advertise at all during the Super Bowl.

Furthermore, the ad agency analysts have concluded that the probabilities of a dull game, average game, above average game, and an exciting game, are, respectively, 0.20, 0.40, 0.30, and 0.10.

The above information has the full the concurrence of marketing analysts on the Directors staff. The Director of Marketing of XYZ must make the decision for how many commercials to buy.

Number of

Commercials Fan Perception of Excitement

Dull Average Above Average Exciting

One -2 3 7 13

Two -5 6 12 18

Three -9 5 13 22

NOTE:In parts 13 and 23 you MUST provide copies of your tables and of your Excel spreadsheet containing your calculations for this problem to receive credit for problem B. You are also reminded to submit all of your computer files for this problem with your completed exam to the Final Exam link on Bb. Failure to provide any of these deliverables will result in this problem NOT being scored.

13.Construct the regret table for this decision situation.

In a new space created below this part, you must present your regret table HERE.

14.a.In new lines entered below this part, state the best (that is, the optimal) decision alternative if the XYZ Marketing Director is basing it on the profit that can be expected.

b. In new lines entered below this part, state the dollar amount of the profit indicated from using this decision-making criterion.

15.a.In new lines entered below this part, state the best decision alternative indicated if the XYZ Marketing Director is basing it on the maximum likelihood criterion.

b. In new lines entered below this part, state the dollar amount of the profit indicated from using this decision-making criterion.

16.In new lines entered below this part, answer the following question: Are the decisions alone (not including the payoffs) of parts 14 and 15 the same? (Yes or no.) Whether they agree or not, explain why. (Failure to explain why will be penalized.)

17.a.In new lines entered below this part, state the best decision if the XYZ Marketing Director is an optimist.

b.In new lines entered below this part, state the dollar amount of the profit indicated from using this decision-making criterion.

18.a.In new lines entered below this part, state the best decision if the XYZ Marketing Director wants to minimize his largest possible regrets.

b.In new lines entered below this part, state the dollar amount of the profit indicated from using this decision-making criterion.

19.a.In new lines entered below this part, state the best decision if the XYZ Marketing Director is a pessimist.

b.In new lines entered below this part, state the dollar amount of the profit indicated from using this decision-making criterion.

20.The XYZ Marketing Director wants to hedge the difference between optimism and pessimism.

a.1.In new lines entered below this part, state the best decision if the XYZ Marketing Director uses a coefficient of optimism with the value 0.75.

2.In new lines entered below this part, state the dollar amount of the profit indicated from using this decision-making criterion.

b.1.In new lines entered below this part, state the best decision if the XYZ Marketing Director uses a coefficient of optimism with the value 0.25.

2.In new lines entered below this part, state the dollar amount of the profit indicated from using this decision-making criterion.

21.In new lines entered below this part, state the dollar amount of value of perfect information.

22.a.In new lines entered below this part, state the dollar amount the XYZ Marketing Director should at most pay to improve the decision over the best decision found in part 14 above.

b.If an outside financial consultant offers the Director of Marketing a better analysis at a price of $3M, should the Director accept?

23.In a new space created below this part, you must present HERE a copy of your Excel spreadsheet for problem B.

AND submit all of your computer files for this problem with your completed exam to the Final Exam link on Bb. Include in the filename/tab name Prob B.

C.The management at XYZ Corporation needs to know the profit per unit sold of a new product. The new product is priced to sell for $45 per unit. The costs incurred in bringing this new product to market are for production, labor, and transportation (shipping). Empirical probability distributions for the purchase cost, labor cost, and transportation cost (all on a per unit basis) are as follows:

Note: Profit = Selling Price - Purchase Cost - Labor Cost - Transportation Cost

NOTE:In parts 25 and 28 you MUST provide a copy of your Excel simulation and of your Excel calculations for problem C to receive credit for this problem. You are also reminded to submit all of your computer files for this problem with your completed exam to the Final Exam link on Bb. Failure to provide any of these deliverables will result in this problem NOT being scored.

24.a. In new lines entered below this part, state the calculated profit per unit for the base-case using the most likely costs.

b.In new lines entered below this part, state the calculated profit per unit for the best case.

c. In new lines entered below this part, state the calculated profit per unit for the worst case.

25.Simulate the profit per unit by performing 20 random trials for each individual cost.

In a space created below this part, you must present HERE a copy of your Excel simulation for problem C.

AND submit all of your computer files for this problem with your completed exam to the Final Exam link on Bb. Include in the filenames Prob C.

26.On the basis of your simulation in part 25,

a. In new lines entered below this part, state to the nearest penny the mean profit per unit.

b.In new lines entered below this part, state to the nearest penny the profit variability per unit as measured by the standard deviation.

c. In new lines entered below this part, state to the nearest penny the lower limit of the 95% confidence interval for mean profit.

d.In new lines entered below this part, state to the nearest penny the upper limit of the 95% confidence interval for mean profit.

27.Management believes that this product will not be sufficiently profitable to warrant the investment in bringing it to market if the profit is less than $5 per unit. On the basis of your simulation, is the product profitable enough to satisfy managements criterion? Explain.

28.In a space created below this part, you must present HERE a copy of your Excel spreadsheet for problem C.

AND submit all of your computer files for this problem with your completed exam to the Final Exam link on Bb. Include in the filename/tab name Prob C.

D.The Pioneer Software Company has developed software for organizing and playing music on a computer. The software contains a number of unique features that have been patented so the companys future has looked bright.

However, it appears that a number of the patented features were copied in similar software developed by the Raider Digital Company, a huge software company with annual sales revenue in excess of $1 billion. The executives of Pioneer Software are distressed that Raider Digital has stolen their ideas; they fear that Raiders marketing power is likely to enable it to capture the market and drive Pioneer out of business.

In response, Pioneer has filed a lawsuit against Raider for patent infringement. With attorney fees and other expenses, the cost of going to trial (win or lose) is expected to be $1 million. Pioneer feels that it has a 60% chance of winning the case, in which case it would receive $5 million in damages. If Pioneer loses the case, it gets nothing. Moreover, if Pioneer loses the case, there is a 50% chance that the judge would also order Pioneer to pay for court expenses and lawyer fees for Raider (an additional $1 million cost).

Raider has countered by offering Pioneer $1.5 million to settle this case out of court.

Using decision tree analysis, determine in the steps below what Pioneer Software Company should do.

NOTE:In parts 29 and 31 you MUST provide a copies of decision tree and of your Excel calculations, respectively, for problem D to be graded. You are also reminded to submit all of your computer files for this problem with your completed exam to the Final Exam link on Bb. Failure to provide any of these deliverables will result in this problem NOT being graded.

29.Draw the decision tree for this problem and annotate it with the expected monetary values where appropriate.

In a space created below this part, you must present HERE a copy of your fully-annotated decision tree.

30.a. In new lines entered below this part, state the decision that the Pioneer Software Company should make.

b.In new lines entered below this part, briefly state the criterion that was used to arrive at this decision.

31.In a space created below this part, you must present HERE a copy of your Excel calculations for problem D.

AND submit all of your computer files for this problem with your completed exam to the Final Exam link on Bb. Include in the filename/tab name Prob D.

E.XYX Manufacturing produces high-end aircraft parts. Their Landing Gear Shop has four machines to make precision airfoil parts: a metal lathe, a turning machine, a milling machine, and a radial drill. This shop has six machine machinists, most of them are certified to work on all the machines and have demonstrated that they perform better on some machines than on others. The Landing Gear has been tasked with a big job that requires all four machines. The times required by the machinists to perform the required work on each machine is given in the table below.

Machinist Operating Time (minutes)

Metal lathe Turning machine Milling machine Radial drill

1 34 16 51 21

2 56 37 32 43

3 27 65 52

4 36 22 53 25

5 45 39 57 31

6 28 32 49 36

Note that Machinist 3 has not yet been certified on the turning machine. As a result, the shop manager will not assign this machinist to that machine.

The shop scheduler needs to schedule a machinist to each machine to produce parts in the least total time.

NOTE:In part 36 you MUST provide your Excel file or Lingo input and output files for problem E to receive credit for this problem. You are also reminded to submit all of your computer files for this problem with your completed exam to the Final Exam link on Bb. Failure to provide any of these deliverables will result in this problem NOT being scored.

In new lines entered below, formulate and state the full and complete mathematical representation of this situation; include specific definitions of all the model variables.

In lines entered below, (1) state the specific class of problem this is and (2) state the specific type of problem this is within that class. Include an explanation of why.

In new lines entered below, state the optimal assignment of a machinist to each machine.

In new lines entered below, state the combined time in minutes expected to produce a part using all four machines with the assigned operators.

In a space created below this part, you must present HERE a copy of your computer input and output screens for problem E.

AND submit all of your computer files for this problem with your completed exam to the Final Exam link on Bb. Include in the filenames/Excel tab names Prob E.