Business 22410 | Course Paper

Unlock access to all the studying documents.

View Full Document

The minimal spanning tree problem is to connect all nodes in a network so that the total

branch lengths are minimized.

The appropriate criterion is dependent on the risk personality and philosophy of the

decision maker.

The first derivative of a cost function equals zero at the point V = 100. This is definitely

the worst output volume for the producer to choose.

The production planner for Airbus showed his boss the latest product mix suggestion

from their slick new linear programming model: 12.5 model 320s and 17.4 model 340s.

The boss looked over his glasses at the production planner and reminded him that they

had several half airplanes from last year’s production rusting in the parking lot. No one,

it seems, is interested in half of an airplane. The production planner whipped out his red

pen and crossed out the .5 and .4, turning the new plan into 12 model 320s and 17

model 340s. This production plan is definitely feasible.

Goal programming provides a method for simultaneously striving to achieve several

objectives.

The Lagrange multiplier is analogous to the dual variables in a linear programming

problem.

Starting conditions have no impact on the validity of a simulation model.

In the method of Lagrange multipliers, the model constraints are multiplied by

Lagrange multipliers and subtracted from the objective function.

Linear programming problems can model decreasing marginal returns.

Irregular variations exhibit no pattern.

There is just as great a chance of a normally distributed random variable being over one

standard deviation above the mean as there is being one standard deviation below the

mean.

An infeasible solution is ensured by rounding down non-integer solution values.

In Bayesian analysis, additional information is used to alter the conditional probability

of the occurrence of an event.

In real-world queuing applications, the multiple-server system analysis techniques are

the same whether customers wait in one line or in separate lines due to customer

balking.

The transshipment model includes intermediate points between the sources and

destinations.

The terms shadow price and dual price mean the same thing.

In a pairwise comparison, two alternatives are compared according to a criterion and

one is preferred.

Proportionality means the slope of a constraint is proportional to the slope of the

objective function.

Most computer linear programming packages readily accept constraints entered in

fractional form, such as X1/X3.

The number of nodes considered in a branch and bound tree for maximization integer

programming problems is always minimized by going to the node with the largest upper

bound.

The value of the game is the offensive player’s gain and the defensive player’s loss in a

zero-sum game.

In PERT, the project variance is the sum of the variance of all project activities.

The shortest route problem requires that there be a branch from each destination to

every other destination.

An optimal solution to a nonlinear programming problem will always occur at the

boundary of the feasible solution space formed by the constraint.

The simplex method is a general mathematical solution technique for solving linear

programming problems.

The Lagrange multiplier is analogous to the dual variables in a linear programming

problem.

A seasonal pattern is an up-and-down repetitive movement within a trend occurring

periodically.

A prohibited route in a transportation model should be assigned an arbitrarily high cost

coefficient.

In computer mathematical simulation, a system is replicated with a mathematical model

that is analyzed with the computer.

The optimal solution for a graphical linear programming problem is the corner point

that is the farthest from the origin.

Transportation problems can be solved by the simplex method.

A linear programming problem requires a choice between alternative courses of action.

The dependent variable in linear regression is usually designated as the x variable.

Sensitivity ranges can be computed only for the right-hand sides of constraints.

In a given experiment, the probabilities of all mutually exclusive events sum to one.

The reorder point is the date when a new order should be placed.

On an AOA diagram, a ________ represents the beginning and end of activities,

referred to as events.

A) path

B) arc

C) branch

D) node

In a balanced transportation model where supply equals demand:

A) all constraints are equalities.

B) none of the constraints are equalities.

C) all constraints are inequalities.

D) none of the constraints are inequalities.

The Vacation

Final exams are almost here and once they are done, it will be time to reward myself

with a well-deserved vacation. As a state employee, I haven’t seen a raise since… well,

ever. Thus an important criterion, in fact the most important criterion is to find an exotic

region that can be visited inexpensively. There are three states of nature that could

impact costs in these five areas of interest, and they correspond to the relative strength

of the US Dollar against that region’s dominant currency. Rather than squander my time

doing any actual publishable research, instead I have determined the average cost per

day to visit each region under each of the possible states of nature. This table, which

should not be construed as actual vacation advice, appears below.

What does the coefficient of optimism need to exceed in order for the Galapagos

Islands to not be the vacation destination of choice?

A) 80

B) 77

C) 74

D) 71

A graduate research assistant “moonlights” at the short order counter in the student

union snack bar in the evenings. He is considering asking for help taking orders, but

needs to convince the management that they should hire another student. Because he is

taking a simulation class, he thinks it may be the perfect way to convince management

to hire more help if he can show that customers have to wait a long time. When a

customer arrives, he takes their order and their payment, prepares the food, gives it to

the customer, and then takes the order from the next person in line. If someone arrives

while he’s cooking an order, they have to wait until he’s completed the current order. He

has simulated 5 orders.

Average customer waiting time is:

A) 1 minute.

B) 2 minutes.

C) 2.5 minutes.

D) 3 minutes.

Use the following table and the information to answer the questions below.

In the following transportation matrix, all cells except 2C have been evaluated and

show no improvement. Evaluate that cell.

Consider the following transportation tableau which shows the initial solution. Evaluate

the cost of allocating units to cell CR.

A) -12

B) -9

C) -6

D) -2

E) +3

A professor’s son, having made the wise decision to drop out of college, has been

finding his way in life taking one job or another, leaving when his creativity is overly

stifled or the employer tires of his creativity. The professor dutifully logs the duration of

his son’s last few careers and has determined that the average duration is normally

distributed with a mean of eighty-eight weeks and a standard deviation of ten weeks.

The next career begins on Monday; what is the likelihood that it endures for more than

two years?

A) 8.5%

B) 7.5%

C) 6.5%

D) 5.5%

Bayesian analysis involves a(n) ________ probability.

A) a priori

B) posterior

C) joint

D) relative frequency

A fair die is rolled nine times. What is the probability that an odd number (1, 3, or 5)

will occur less than 3 times?

A) .0899

B) .2544

C) .7456

D) .9101

The ________ and variance are derived from a subset of the population data and are

used to make inferences about the population.

A) population variance

B) population standard deviation

C) population mean

D) sample mean

Given the nonlinear programming model:

Max Z = 5x1 – 2x2

Subject to: x1 + x2 = 6

What is the optimal value of the objective function?

A) Z = 19.625

B) Z = 20.625

C) Z = 21.625

D) Z = 22.625

E) Z = 23.625

The Deadbeats

After months of broken promises, partial payments, and general stupidity, the landlord

had no choice but to evict the long term tenants that had become little more than

squatters in his first rental property. As he surveyed the damage and pondered a mix of

repairs an upgrades, he scoured the latest statistics on what Different upgrades might be

worth in terms of increased rent. Beautifully refinished wood floors could increase the

monthly rent about $100 and an upgrade to the kitchen would fetch $80 per month. The

garage door needed replacement, but even though it would receive daily use, it was

almost an order qualifier, and wouldn’t net more than $20 per month. The house had

always suffered from lack of a back door you had to access the backyard through the

garage, so taking out a window and replacing it with a safety door would cost $250 and

add only $15 to the monthly rent. The garage door would cost $350, the kitchen update

would cost $1000 if he went with granite, and the floor refinish job would cost $400 to

rent the buffer and buy the chemicals. It wouldn’t be easy doing these upgrades; the

garage door would take a half week, the back door one week, the floors two weeks and

the tile three weeks.

There was another way around these jobs though; instead of doing them himself, the

landlord could always hire a professional in each field that could finish the job in half

the time but would charge a pretty penny for that speed. Refinishing floors would cost

$2700, upgrading the kitchen would cost $2500, replacing the back window with a door

would cost $600, and installing a garage door opener would cost $350.

Obviously if the model wants to upgrade the kitchen, it should be done by either the

landlord or a subcontractor. As he creates the IP model, the landlord wants to leave the

choice of whether to actually upgrade the kitchen up to the optimization algorithm.

How should this constraint be written if he uses the following scheme for decision

variables?

A) x3 + x4 ≤ 1

B) x3 + x4 = 1

C) x3 – x4 ≤ 1

D) x3 – x4 = 1

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.

Which of these is not an element of the objective function?

A) 4DF

B) 600D

C) 9EG

D) 3CE

Figure 2

Consider the optimization problem represented by this graph. The objective function is

represented by line GH. Where is the optimal solution?

A) the intersection of lines AB and EF

B) the intersection of lines AB and CD

C) the intersection of lines CD and EF

D) the upper right corner of the shaded region

The expected value of the standard normal distribution is equal to:

A) 0

B) 1

C) 1.5

D) 2

The difference between the assignment and the transportation problem is that:

A) total supply must equal total demand in the assignment problem.

B) the number of origins must equal the number of destinations in the transportation

problem.

C) each supply and demand value is 1 in the assignment problem.

D) both A and B

Cars arrive at a single-bay car wash at an average of 6 per hour according to the Poisson

distribution. The wash time averages 4 minutes with a standard deviation of 1 minute,

but the wash time is not defined by any distribution. What is the average number of cars

in line?

A) .142

B) .267

C) .283

D) 2.83

________ probability is an estimate based on personal belief, experience, or knowledge

of a situation.

A) Binomial

B) Subjective

C) Marginal

D) Joint

Jolt – M

The soda machines outside the lecture hall sees a steady stream of customers

throughout the day. Between the student’s use of the machine and the mechanism, it

takes 15 seconds (exponentially distributed) to deliver a can of carbonated sugar water

to a thirsty customer. Over the course of a twelve hour lecture day, students arrive at the

rate of 450 per hour.

The soda machines have become self aware and when they are not in use dispensing

ice-cold beverages, they are busy formulating a plan for world domination. About how

much time over the course of a week can they develop their battle plans?

A) 84 hours

B) 89 hours

C) 94 hours

D) 99 hours

Which one of the following management science methods is nota probabilistic

technique?

A) assignment models

B) decision analysis

C) queuing analysis

D) statistical analysis

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 finish time for activity A?

A) 9

B) 10

C) 11

D) 12

After plowing through contracts for a decade, the contract writer knew about how long

it took to crank out the material necessary to satisfy a contract’s requirements. The

distribution could be modeled using the data provided in this table.

Using the random number table 14.3 in your text, column 1, reading across row 6, what

is the average length of the next five contracts?

A) 4.6

B) 4.4

C) 4.2

D) 4.0

With the ________ criterion each player seeks to minimize maximum possible losses.

A) minimax

B) maximax

C) minimin

D) maximin

The local soda machines union has some concerns regarding how busy these two

machines are. They have work rules that demand that machines can be no busier than

working half of their scheduled work shift. How many machines should be employed to

bring them in line with the utilization rule?

A) 1 machine

B) 2 machines

C) 3 machines

D) 4 machines

Jolt – K

The soda machine outside the lecture hall sees a steady stream of customers throughout

the day. The machine takes 4 seconds to deliver a can of carbonated sugar water once

the button is pressed and students generally know what they want from the machine –

the average feeding of the machine takes two seconds. Over the course of a twelve hour

lecture day, students arrive at the rate of 500 per hour.

The soda delivery guy stocks up the machine at the start of each day. How many cans of

soda will he need to stock up the machine each morning?

A) 600

B) 720

C) 6,000

D) 7,200

The Krewe of Orpheus

The Krewe of Orpheus maintains a supply of swizzle sticks for events throughout the

year. Demand for swizzle sticks is shockingly low, a quick check of krewe records from

last year reveals that they used only 585,000, but the krewe president believes that they

should be good stewards of what they have, so they seek to manage this inventory using

the EOQ policy, although they prefer to refer to it as an EOKrewe policy for obvious

reasons. Swizzle sticks are not expensive items, they cost a nickel apiece largely due to

the club logo printed on each one. This also serves to increase the lead time as they

can’t be obtained from a standard restaurant supply house. Instead, they must be ordered

with an eye towards the six day lead time. It costs $15 to place an order, most of this

cost is a result of explaining the meaning of “Laissez les bons temps rouler” and why it

should be printed on the edge of each swizzle stick. Holding cost is 20% of purchase

price.

How many orders will they place in a year if they order optimally (in accordance with

the EOQ policy)?

A) about 8

B) about 10

C) about 12

D) about 14

Napoleon is contemplating four institutions of higher learning as options for a Masters

in Business Administration. Each university has strong and weak points and the demand

for MBA graduates is uncertain. The availability of jobs, student loans, and financial

support will have a significant impact on Napoleon’s ultimate decision. Vanderbilt and

Seattle University have comparatively high tuition, which would necessitate Napoleon

take out student loans resulting in possibly substantial student loan debt. In a tight

market, degrees with that cachet might spell the difference between a hefty paycheck

and a piddling unemployment check. Northeastern State University and Texas Tech

University hold the advantage of comparatively low tuition but a more regional appeal

in a tight job market. Napoleon gathers his advisory council of Kip and Pedro to assist

with the decision. Together they forecast three possible scenarios for the job market and

institutional success and predict annual cash flows associated with an MBA from each

institution. All cash flows in the table are in thousands of dollars.

Suppose that the likelihood for each of the scenarios 1 through 3 is 0.3, 4, and 0.3,

respectively. What is the optimal decision under the expected opportunity loss criterion?

A) Vanderbilt University

B) Texas Tech University

C) Seattle University

D) Northeastern State University

Kushie’s Coffee in Bangalore is a quaint establishment nestled near MG Road in the

central business district. It serves coffee and fruit cake to a clientele that has been

enjoying these products for over fifty years. The demand for coffee beans is 6600 cases

per year (each case has 24 ten-pound bags). It would be disastrous for them to run out

of coffee, so they keep a safety stock of 30 cases. The cases cost $4800 and it costs $5

per case to order coffee. As coffee is a perishable product, the holding cost is fairly high

at $40/case/year. The lead time to receive an order is seven days. Kushie’s is open 300

days a year.

What is their annual ordering cost if they order at their EOQ level?

A) 101.6

B) 203.1

C) 406.2

D) 812.4

Values with an acceptable consistency ratio are values:

A) less than or equal to 0.1.

B) greater than 0.5 but less than 0.6.

C) less than 1 but greater than 0.5.

D) greater than 0.2 but less than 0.5.

Which of the following can be used to solve integer programs with 2 variables?

I. Graphical techniques

II. Complete enumeration

III. Relaxed LP solutions

IV. Branch and bound

A) I, II, III, and IV

B) I and III

C) I, II, and IV

D) I and IV

E) I, II and III

A company plans to use an automatic guided vehicle for delivering mail to ten

departments. The vehicle will begin from its docking area, visit each department, and

return to the docking area. Cost is proportional to distance traveled. The type of

network model that best represent this situation is ________.

Which of the following would not be considered a limitation of simulation modeling?

A) Models are typically unstructured.

B) Validation of simulation models can be Difficult.

C) The cost of building simulation can be prohibitive.

D) Simulation allows flexibility in analyzing systems.

Armed only with his fingers, the owner decides that the safest forecasting approach is

exponential smoothing with an alpha of 0.8. He uses the January demand and the

January forecast just to get the ball rolling. Generate a forecast for the year using this

technique and then calculate forecast errors using MSE. What is the mean squared error

for this forecasting approach?

A) 4013

B) 3686

C) 3462

D) 3840