BUS 56071 | Course Paper

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A point of equilibrium is a value that is simultaneously the minimum of a row and the

maximum of a column.

A posterior probability is the likelihood that an event has occurred after the decision

maker has reached a decision.

A Markov assumption is that the probabilities change over time.

A Markov assumption is that the probabilities apply to all system participants.

Markov analysis is not an optimization technique.

A management science technique usually applies to a specific model type.

The Lagrange multiplier reflects a change in the objective function from a unit change

in the right-hand-side value of a constraint.

The basic feasible solution in the initial simplex tableau is the origin where all decision

variables equal zero.

Random numbers are typically generated on the computer using a numerical technique.

The Hurwicz criterion multiplies the worst payoff by the coefficient of optimism.

Sensitivity analysis can be used to determine the effect on the solution for changing

several parameters at once.

Applications of simulation models reflecting continuous distributions are more common

than those of models employing discrete distributions.

Assignment linear programs always result in integer solutions.

The following equation represents a resource constraint for a maximization problem: X

+ Y ≥ 20.

Markov analysis provides a recommended decision.

Adjusted exponential smoothing is an exponential smoothing forecast adjusted for

seasonality.

All single-server queuing models require the utilization factor to be less than 1.

The state of the system is where the system is at a point in time.

Queue discipline refers to the willingness of customers to wait in line for service.

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a

mutually exclusive constraint.

Transportation problems can have solution values that are non-integer and must be

rounded.

Data envelopment analysis problems are usually maximization problems.

Simulation results will always equal analytical results if 30 trials of the simulation have

been conducted.

The earliest finish time for the final activity on a project network is also the total

completion of the project.

A negative deviational variable is the amount by which a goal level is exceeded.

The slope of a curve at any point is equal to the derivative of the curve’s function.

Decision trees can be used to solve for steady state probabilities.

The equation 8xy = 32 satisfies the proportionality property of linear programming.

An experiment is an activity that results in one of several possible outcomes.

Multiple optimal solutions cannot be determined from the simplex method.

Consider the following integer programming problem. Solve it using the branch and

bound method. What are the optimal values of x1, x2, and Z?

Maximize Z = 2x1 + x2

Subject to: 2x1 + 2x2 ≤ 7

4x1 + x2 ≤ 11

x1 and x2 ≥ 0

A) x1 = 1, x2 = 2, Z = 4

B) x1 = 2, x2 = 1, Z = 5

C) x1 = 1, x2 = 1, Z = 3

D) x1 = 0, x2 = 3, Z = 3

E) x1 = 2, x2 = 2, Z = 6

The slope of a curve at any point is ________ the derivative of the curves function.

A) smaller than

B) larger than

C) equal to

D) none of the above

A Markov assumption is that the probabilities apply to ________ system participants.

A) none of the

B) the major

C) some

D) all

In the linear programming formulation of a transportation network:

A) there is one variable for each arc.

B) there is one constraint for each node.

C) the sum of variables corresponding to arcs out of an source node is constrained by

the supply at that node.

D) all of the above

What is the reorder point for Stein soda?

A) 4 cases

B) 8 cases

C) 12 cases

D) 16 cases

Yowzah Bids

Yowzah receives bids from four companies we’ll call A, B, C, and D to supply product

for the coming year. Renee DeCartes, the Yowzah VP of Plotting takes the bids and

creates this graph to bring to the next executive meeting.

Company A has a fixed cost of 75,000 and a variable cost of 15. Company B’s fixed

cost is 90,000 and variable cost is 11. At what point is Yowzah indifferent between the

two bidders?

A) 3,250

B) 3,500

C) 3,750

D) 4,000

A single-server waiting line system has an arrival pattern characterized by a Poisson

distribution with 3 customers per hour. The average service time is 12 minutes. The

service times are distributed according to the negative exponential distribution.The

probability that the system is idle is:

A) 0

B) .20.

C) .40.

D) .60.

The derivative of a function ________ the slope of the curve defined by that function.

A) is larger than

B) equals

C) is smaller than

D) is similar to

The Hurwicz criterion is a compromise between the minimax and minimin criteria.

A university is planning an online seminar. It costs $30 to live stream an instructor from

Elbonia. Assume it costs $25 per student for the administrators to provide the course

materials. If we know that 20 people will attend, what price should be charged per

person to break even?

A) $55

B) $15

C) $26.50

D) $75.75

A retired operations management professor moves to New Orleans, joins the Krewe of

Orpheus and convinces krewe leadership to buy their own swizzle stick production

equipment. They invest in a medium-scale machine called the Swizzo 2025, which is

capable of producing swizzle sticks at the rate of 1800 per day. How long does it take to

produce the optimal batch size?

A) 10 weeks

B) 9 weeks

C) 8 weeks

D) 7 weeks

If Xab = the production of product a in period b, then to indicate that the limit on

production of the company’s 3 products in period 2 is 400, we write:

A) X32 ≤ 400.

B) X21 + X22 + X23 ≤ 400.

C) X12 + X22 + X32 ≤ 400.

D) X12 + X22 + X32 ≥ 400.

Riverside Industries makes two products and each product is processed in three

departments. The time requirements for each product in each department are given

below. The profit for each product is also provided as well as the available hours in

each department.

Product Department A Department B Department C Profit

1 3 4 2 1

2 2 1 2 2

Available Hours 600 400 400

Management wants to achieve three goals. The first two goals are equal in priority.

Priority 1: Produce at least 125 units of product 1.

Priority 1: Produce at least 80 units of product 2.

Priority 2: Achieve a profit of at least 300.

The goal programming constraint for the first goal is:

A) 3x1 + d1

– – d1

+ = 125.

B) 3x1 – d1

– + d1

+ = 125.

C) 1x1 + d1

– – d1

+ = 125.

D) 1x1 – d1

– + d1

+ = 125.

Yowzah Bids

Yowzah receives bids from four companies we’ll call A, B, C, and D to supply product

for the coming year. Renee DeCartes, the Yowzah VP of Plotting takes the bids and

creates this graph to bring to the next executive meeting.

Over the range of demand shown by this graph, which action would completely remove

one of the potential suppliers from consideration?

A) lowering A’s fixed cost by 10%

B) raising B’s variable cost by 10%

C) raising C’s variable and fixed costs by 10%

D) lowering D’s fixed cost by 25%

A small entrepreneurial company is trying to decide between developing two different

products that they believe they can sell to two potential companies, one large and one

small. If they develop Product A, they have a 50% chance of selling it to the large

company with annual purchases of about 20,000 units. If the large company won’t

purchase it, then they think they have an 80% chance of placing it with a smaller

company, with sales of 15,000 units. On the other hand if they develop Product B, they

feel they have a 40% chance of selling it to the large company, resulting in annual sales

of about 17,000 units. If the large company doesn’t buy it, they have a 50% chance of

selling it to the small company with sales of 20,000 units.

What is the probability that Product A will being purchased by the smaller company?

A) 0.8

B) 0.5

C) 0.4

D) 0.2

Companies A, B, and C supply components to three plants (F, G, and H) via two

crossdocking facilities (D and E). It costs $4 to ship from D regardless of final

destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C

costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and

$8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively

and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D

and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin,

had previously used “Chain of Fools” as her supply chain consulting company, but now

turns to you for some solid advice.

How many constraints are required to model this as a linear program?

A) 8

B) 9

C) 10

D) 12

Cold & Calculating

The cold, calculating father did exactly that when examining the 27 year old failure to

launch man child that had turned his walk in closet into a bedroom. As he saw it, there

were five alternatives; each had its advantages and disadvantages, and under different

circumstances, each had a different financial incentive. He laid it all out neatly in a

table, but as not to arouse suspicion, he left the table’s labels very generic, so the

alternatives were simply labeled A through E while the different circumstances were

simply numbered one through three. He flicked the gray ash off of his favorite purple

smoking jacket and pondered the best course of action under each possible future. It

was good to be devious, he decided.

The appropriate criterion is dependent on:

A) the risk personality of the decision maker.

B) the number of nodes in the decision tree.

C) the magnitude of the payoffs.

D) none of the above

A business owner is trying to decide whether to buy, rent, or lease office space and has

constructed the following payoff table based on whether business is brisk or slow.

The maximin strategy is:

A) Buy.

B) Rent.

C) Lease.

D) Brisk.

The following table represents the cost to ship from Distribution Center 1, 2, or 3 to

Customer A, B, or C.

The constraint that represents the quantity demanded by Customer B is:

A) 6X1B + 2X2B + 8X3B ≤ 350.

B) 6X1B + 2X2B + 8X3B = 350.

C) X1B + X2B + X3B ≤ 350.

D) X1B + X2B + X3B = 350.

The manager is open to suggestions for forecasting models. Plot the data and discuss

the efficacy of the moving average, weighted moving average, exponential smoothing,

and trend as the relate to this data.

The gentleman farmer kept chickens for the eggs, the splash of color in the yard, and

because he found their gentle clucking to relax him as he worked on his laptop on his

deck. Their movements around his yard gave meaning to the term random walk you

literally could not predict their location from one minute to the next. His collection of

birds is neatly summarized in this table.

A hen just joined him up on the deck; what is the probability it is an Australorp?

A) 0.18

B) 0.20

C) 0.22

D) 0.24

A 95% confidence interval is (54.5, 57.5) based on a sample size of What is the sample

standard deviation?

A) 3.826

B) 19.132

C) 8.973

D) 11.646

In multiple-server models, ________ independent servers in parallel serve a single

waiting line.

A) 2 or more

B) 3 or more

C) 4 or more

D) 5 or more

Project Sand Mandala

Carrie meticulously calculated the early and late start and finish times for her latest

project and recorded them using different colors of sand on a pristine slab of white

marble. She used red for late start and late finish times and green for early start and

early finish times. Activity durations and their identifiers were written with black sand.

She finished her task and had an opportunity to admire her work only briefly before a

colleague came by and swept most of it away. Sadly, this was before Carrie could

record the numbers on a more permanent medium, so now she turns to you to help.

What is the late start time for activity H?

A) 21

B) 24

C) 17

D) 23

Zevon Enterprises

Zevon Enterprises provides services for clients worldwide and to protect all parties to

this course as well as Zevon, we shall refer to those services as X1, X2, and X3. Each of

these services has its own special mix of needs for the resources the company has at its

disposal. The X1 product requires three lawyers, seven guns, and $6,000; the X2

product requires two lawyers, five guns, and $4,000; and the X3 product requires four

lawyers, six guns, and $7,000. Zevon has access to 5,000 lawyers, 10,000 guns, and

$15,000,000. For ease of conversation, Zevon employees usually speak about dollars as

“per thousand” so one of them asking for $7 means that they really need $7,000.

Zevon’s demand is variable depending on what they charge for it. For example, the X1

product’s demand is 200 – 2.25p1. The demand for X2 is 300 – 3p2, and the demand for

X3 is 400 – 3.5p3. The per unit profit forX1 through X3 can be calculated by subtracting

the per unit cost from the sales price, so for X1, the profit is p1 – 25, for X2 the profit is

p2– 3, and for X3 the profit is p3– 3.5.

What is an appropriate objective function for this scenario?

A) Max Z = (p1– 2.25)X1 + (p2– 3)X2 + (p3– 3.5)X3

B) Max Z = (p1– 2.25)(200 – 2.25p1) + (p2– 3)(300 – 3.00p2) + (p3– 3.5)(400 – 3.50p3)

C) Max Z = 200X1 + 300X2 + 400X3

D) Max Z = 2.25(p1– X1) + 3(p2– X2) +3.5 (p3– X3)

What is the proper interpretation of the shadow price for Facebook?

A) Every additional dollar spent on Facebook advertising gains 20 customers as long as

the number of postings does not exceed 233.

B) Every additional dollar spent on Facebook advertising gains 20 customers as long as

the number of postings does not exceed 229.

C) If they spend $4, then can reach 20 customers.

D) If they spend less than $20, they can reach 229.333 customers.

If the number of unique assignments is ________ the number of rows or columns, a line

test must be used.

A) more than

B) less than

C) higher than

D) equal to

Dinnertime

A professor is planning an informal gathering for 100 or so of his closest friends. The

project breaks down as follows:

Which activity has a slack time that is different from all others?

A) hire quartet

B) hire valets

C) schedule butler

D) schedule cleaning crew

Project Sand Mandala

Carrie meticulously calculated the early and late start and finish times for her latest

project and recorded them using different colors of sand on a pristine slab of white

marble. She used red for late start and late finish times and green for early start and

early finish times. Activity durations and their identifiers were written with black sand.

She finished her task and had an opportunity to admire her work only briefly before a

colleague came by and swept most of it away. Sadly, this was before Carrie could

record the numbers on a more permanent medium, so now she turns to you to help.

What is the slack time for activity C?

A) 3

B) 2

C) 1

D) 0

The Lagrange multiplier reflects the appropriate change in the objective function

resulting from a unit change in the ________ of the constraint equation.

A) coefficient

B) objective function

C) right-hand side

D) shadow price

Construct the payoff matrix for the game, “rock, paper, scissors” for 2 players, A and B.

Assume that “paper covers rock,” “rock breaks scissors,” and ‘scissors cut paper.” If

player A wins, assign +1. If player A loses, assign -1.

________ is the analysis of the effect of parameter changes on the optimal solution.