DSCI Final Review

Infeasibility means that the number of solutions to the linear programming models that satisfies all the problem's constraints is

0

Consider a project that has an expected completion time of 60 weeks and a standard deviation offive weeks. What is the probability that the project will take anywhere between 60 and 65 weeks to complete? (Round to two decimals.)

0.34

At a local fast-food joint, cars arrive randomly at a rate of 3 every 30 minutes. The fast food joint takes an average of 4 minutes to serve each arrival. The utilization factor for this system is:

0.4

Looking at the below excel report for an LP problem, Answer the following question: What is the slack for resource "Raw Materials"?

100

The annual demand for a product has been projected at 2,000 units. This demand is assumed to be constant throughout the year. The ordering cost is $20 per order, and the holding cost is 20 percent of the purchase cost. Currently, the purchase cost is $40 per unit. There are 250 working days per year. Whenever an order is placed, it is known that the entire order will arrive on a truck in 6 days. How many units should the company order each time an order is placed if the company wishes to minimize total inventory cost?

100

Given an activity's optimistic, most likely, and pessimistic time estimates of 4, 14, and 18 days respectively, compute the PERT expected activity time for this activity.

13

Daily demand for newspapers for the last 10 days has been as follows (listed from oldest to newest): 12, 13, 16, 15, 12, 18, 14, 12, 13, 15. Forecast sales for the next day (i.e. day 11) using a two-day moving average.

14

Consider the following linear programming problem: Maximize 12X + 10Y Subject to: 4X + 3Y ≤ 480 2X + 3Y ≤ 360 all variables ≥ 0 The maximum possible value for the objective function is:

1520

Consider the following linear programming problem: Maximize 4X + 10Y Subject to: 3X + 4Y ≤ 480 4X + 2Y ≤ 360 all variables ≥ 0 The feasible corner points are (48,84), (0,120), (0,0), (90,0). What is the maximum possible value for the objective function?

1600

Daily demand for newspapers for the last 10 days has been as follows: 12, 13, 16, 15, 12, 18, 14, 15, 12, 20 (listed from oldest to most recent). Forecast sales for the next day (day 11) using a two-day weighted moving average where the weights are 5 and 3 will be:

17

Consider a project that has an expected completion time of 30 weeks and a standard deviation of 6 weeks. What is the probability that the project will be take more than 42 weeks? (Round answer)

2%

A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution while service times follow an exponential distribution. If the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes, what proportion of the time is the server busy (utilized)?

2.25

Candy Incorporated stocks bubble gum game cards, an item that has a normally distributed demand during the reorder period with a mean of 12 dozen boxes and a standard deviation of 2 dozen boxes. If it is desirable to experience a stockout only 10 percent of the time, what is the appropriate safety stock?

2.56

The annual demand of a certain item is 22,000 units and the computed EOQ is 1,100 units. How many orders do they have to make per year?

20

Emarpy Appliances Inc. wants to determine the optimal production policy for their best selling refrigerator. The demand for this has been relatively constant at about 8,000 each year. The production capacity for this product is limited to 200 units per day. Each time production starts, it costs the company $120 to move materials into place, reset the assembly line, and clean the equipment. The holding cost of a refrigerator is $50 per unit per year. Assume there are 250 working days per year. If Emarpy Inc wants to minimize the total annual inventory cost, how many refrigerators should be produced in each production run?

213.81

A payoff table is given as follows. If the probabilities of s1, s2, and s3 are 0.2, 0.5, and 0.3 respectively, then what would be the EVPI? State of Nature Decision s1 s2 s3 d1 250 750 500 d2 300 −250 1200 d3 500 500 600 Selected Answer:d. 260 Correct Answer:d. 260

260

A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes, what is the average number of customers in the system?

3.00

Candies'r us stocks bubble gum game cards, an item that has a normally distributed demand during the reorder period with a mean of 12 dozen boxes and a standard deviation of 2 dozen boxes. If it is desirable to experience a stockout of only 5 percent of the time, what is the appropriate safety stock? (choose the closest answer to your calculation)

3.28

A large school district is reevaluating its teachers' salaries. They have decided to use regression analysis to predict mean teachers' salaries at each elementary school. The researcher uses years of experience to predict salary. The resulting equation was: Y = 20500 + 1550 X where Y = salary and X = years of experience If a teacher has 24 years of experience, what is the forecasted salary? Enter your answer in the small box below.

57,700 ± 1

The annual demand of a certain item is 5400 units and the computed EOQ is 900 units. How many orders do they have to make per year?

6

Use the following table to answer the following question Activity Immediate Predecessor Time ES EF LS LF A - 4 0 4 6 10 B - 5 0 5 0 5 C A 3 4 7 10 13 D B 8 5 13 5 13 E B 2 5 7 16 18 F C, D 3 13 16 15 18 G C, D 7 13 20 13 20 H E, F 2 16 18 18 20 How long can activity C be delayed without delaying the completion of the project?

6

At an automatic car wash, cars arrive randomly at a rate of 7 cars every 30 minutes. The car wash takes exactly 4 minutes. On average, what would the length of the line be?

6.533

The following represents a project with known activity times. All times are in weeks. Activity Immediate Predecessor Time A - 4 B - 3 C A 2 D B 7 E C, D 4 F B 5 Using the data in Table above, what is the minimum possible time required for completing the project?

8

At a local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes. Service times are random (exponential) and average 2 minutes per arrival. The average time in the queue for each arrival is

8 minutes

Calculate MAD for the following forecast versus actual sales figures. Forecast Actual 100 95 110 108 120 123 130 130

9.5

The following is a payoff table giving COST for various situations. State 1 State 2 State 3 Alternative 1 45 37 83 Alternative 2 16 59 72 Alternative 3 23 65 91 Alternative 4 44 33 55 What decision should be made based on the minimax regret criterion?

Alternative 2

The following is a payoff table giving profits for various situations. What decision would an optimistic person make?

Alternative 2

Given the network in Figure below, the critical path is

B,D,E,G,H

Which of the following is a general rule for crashing activities?

Crash activities with zero slack.

The following table is part of an exponential smoothing forecast. Compute the forecast for November, given that α= 0.4 Notation: (Y= Actual value; F is the forecast value; and e is the error) YtFtetSeptember733718 October744 November

FNov.= 732

An M│M│3 model has Poisson arrivals, exponential service times, and two channels.

False

The variance of the project completion time is equal to the sum of the variances of all the activities.

False

Which of the following statements is true about r2?

It is also called the coefficient of determination

Which of the following methods produces a particularly stiff penalty in periods with large forecast errors?

MSE

A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 15 per hour. It takes an average of two minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed.(be consistent with rates!)Find the probability that the employee is idle.

Po = 0.50

Bias tells us whether the forecast tends to be too high or too low

True

CPM was developed for use in managing projects about which we have good information about activity or task completion times.

True

EVPI (Expected Value of Perfect Information) is a measure of the maximum value of additional information.

True

For any constraint, either its slack/surplus value must be zero or its dual price must be zero

True

If we are studying the arrival of automobiles at a highway toll station, we can assume an infinite calling population.

True

Models that do not involve risk or chance are deterministic problems

True

On a practical note-if we are using waiting line analysis to study cars passing through a single tollbooth, reneging is probably not an issue.

True

One difficulty in waiting line analysis is that it is sometimes difficult to place a value on customer waiting time.

True

Slack is the time an activity can be delayed without impacting the completion time of the project.

True

The best regression model is a statistically significant model with a high r-square and few variables.

True

The set of solution points that satisfies all of a linear programming problem's constraints simultaneously is defined as the feasible region in graphical linear programming.

True

When looking at the arrivals at the ticket counter of a movie theater, we can assume an unlimited queue.

True

Which of the following is not acceptable as a constraint in a linear programming problem?

X + XY + Y >= 12

Given the following Linear Programming Problem MAX 25X1+30X2+15X3S.T. 1) 4X1+5X2+8X3 <=1200 2) 9X1+15X2+3X3 <=1500 X1 and X2 >= 0 Run Excel solver to solve this problem to answer the following question: What is the Maximum Objective Function Value Z?

Z= 4,700

The following is a payoff table giving profits for various situations. What decision would an optimist make? State of Nature Decision s1 s2 s3 d1 10 8 6 d2 14 15 2 d3 7 8 9

d2

The critical path of a network is the

longest time path through the network

Which of the following factors is (are) not included in ordering cost?

obsolescence

A constraint that does not affect the feasible region is a

redundant constraint

Extra inventory that is used to avoid stockouts is known as

safety stock

The term queue discipline describes the

sequence in which members of the queue are serviced.

For an activity with more than one immediate successor activity, its latest-finish time is equal to the

smallest latest-start time among its immediate successors.

The crash time of an activity represents

the shortened activity time

Infeasibility in a linear programming problem occurs when

there is no solution that satisfies all the constraints given.