# GBA 334 Mid-Term Examination

GBA 334 Mid-Term Examination

1. 1.       Sensitivity analysis helps us estimate the effect of known and unknown errors in our model.

True or False?

1. 2.      AnnMcCoy, a student at Tech, plans to open a hot dog stand inside Tech’s football stadium during home games. There are seven home games scheduled for the upcoming season. She must pay the Tech athletic department a vendor’s fee of \$3,000 for the season.  Her stand and other equipment will cost her \$4,500 for the season. She estimates that each hot dog she sells will cost her \$.35. She has talked to friends at other universities who sell hot dogs at games. Based on their information and the athletic department’s forecast that each game will sell out, she anticipate that she will sell approximately 2,000 hot dogs during each game.
1. What price should she charge for a hot dog in order to break even?
2. What factors might occur during the season that would alter the volume sold and thus the break- even price Annie might charge?
3. What price would you suggest that Annie charge for a hot dog to provide her with a reasonable profit while remaining competitive with other food vendors?

3.What is the formula for the break-even point of a simple profit model?

a. Fixed Cost / Variable Cost Per Unit

b. Selling Price Per Unit —Variable Cost Per Unit) / Fixed Cost

c. Fixed Cost / (Selling Price Per Unit —Variable Cost Per Unit)

d. Fixed Cost / (Variable Cost Per Unit — Selling Price Per Unit)

e. Selling Price Per Unit — (Fixed Cost / Variable Cost Per Unit)

4.If fixed cost is \$10,000, variable cost is \$4 and BEP units are 1,000. What is the selling cost?

5.Karen bakes pies for a living. She sells pies for \$15 each. Her monthly fixed costs are \$1200.

Each pie variable costs \$2.50 in materials. Find the break – even number of pies that Karen must

make and sell each month. What is the revenue and cost at this number of pies?

6.Given the following distribution:

 Outcome Value ofRandom Variable Probability A 1 .4 B 2 .3 C 3 .2 D 4 .1

The expected value is 3.

True or False?

7.A new young executive is perplexed at the number of interruptions that occur due to

Employee relations. She has decided to track the number of interruptions that occur during

each hour of her day. Over the last month, she has determined that between 0 and 3

interruptions occur during any given hour of her day. The data is shown below.

 Number of Interruptions in 1 hour Probability 0 interruption .5 1 interruptions .3 2 interruptions .1 3 interruptions .1

On average, she should expect 0.8 interruptions per hour.

True or False?

8.

 Workers Skill Non-skill Union Total Male 50 150 Female 50 Total 100 300
1. What is the probability of non-skill female workers?
2. What is the probability of male workers?
3. What is the probability of union workers?
4. What is the probability of male skill workers?

9.Assume you have a normal distribution representing the likelihood of completion times.

The mean of this distribution is 10, and the standard deviation is 3.  The probability of

completing the project in 8 or fewer days is the same as the probability of completing the

project in 18 days or more.

True or False?

10.A ________ is a numerical statement about the likelihood that an event will occur.

A) mutually exclusive construct

B) collectively exhaustive construct

C) variance

D) probability

E) standard deviation

11.  The decision maker can control states of nature.

True or False?

12.  Expected monetary value (EMV) is the average or expected monetary outcome of a decision

if it can be repeated a large number of times. True or False?

13.  ____________________________________ is a measure of the maximum EMV as a result

14.George Golf is considering the purchase of two types of industrial robots. There are two states of

nature and they are Event 1(favorable) and Event 2 (unfavorable). The probability for Event 1 is 60%.

The probability of Event 2 is 40%. The Rob 1 (alternative 1) is a large robot capable of performing a

variety of tasks, including welding and painting. The payoff for Event 1 for Rob 1 (alternative 1) is

\$50,000. The payoff for Event 2 for Rob 1 (alternative 1) is -30,000. The Rob 2 (alternative 2) is a

smaller and slower robot, but it has all the capabilities of Rob 1. The payoff for Event 1 is \$30,000 for

Rob 2 (alternative 2). The payoff for Event 2 for Rob 2 (alternative 2) is \$-10,000. The robots will be

used to perform a variety of repair operations on large industrial equipment. Of course, George can

always do nothing and not buy any robots (alternative 3). The market for the repair operation could be

favorable (event 1) or unfavorable (event 2).

1. Develop a decision table.
2. Determine what would be the Criterion of Realism criterion if the coefficient of realism is 60%.

1. 15.  Looking at problem  14:
1. What is the Expected Monetary Value?
2. What is the minimum EOL?

1. 16.  A concessionaire for the local ballpark has developed a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd).

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If the probabilities associated with the states of nature are 0.30 for a large crowd, 0.50 for an average crowd, and 0.20 for a small crowd, determine:

(a)        the alternative that provides the greatest expected monetary value (EMV)

(b)        the expected value of perfect information (EVPI)

1. 17.  An LP formulation typically requires finding the maximum value of an objective while simultaneously maximizing usage of the resource constraints. True or False?

1. 18.  A company can decide how many additional labor hours to acquire for a given week. Subcontractor workers will only work a maximum of 20 hours a week. The company must produce at least 200 units of product A, 300 units of product B, and 400 units of product C. In 1 hour of work, worker 1 can produce 15 units of product A, 10 units of product B, and 30 units of product C. Worker 2 can produce 5 units of product A, 20 units of product B, and 35 units of product C. Worker 3 can produce 20 units of product A, 15 units of product B, and 25 units of product C. Worker 1 demands a salary of  \$50/hr., worker 2 demands a salary of \$40/hr., and worker 3 demands a salary of \$45/hr. The company must choose how many hours they should contract with each worker to meet their production requirements and minimize labor cost.

(a) Formulate this as a linear programming problem.

(b) Find the optimal solution.

1. 19.  A plastic parts supplier produces two types of plastic parts used for electronics. Type 1 requires 30 minutes of labor and 45 minutes of machine time. Type 2 requires 60 minutes of machine hours and 75 minutes of labor. There are 600 hours available per week of labor and 800 machine hours available. The demand for custom molds and plastic parts are identical. Type 1 has a profit margin of \$25 a unit and Type 2 have a profit margin of \$45 a unit. The plastic parts supplier must choose the quantity of Product A and Product B to produce which maximizes profit.

(a) Formulate this as a linear programming problem.

(b) Find the solution that gives the maximum profit using either QM for Windows or Excel.

1. 20.  Suppose a linear programming (maximization) problem has been solved and the optimal value of the objective function is \$300.  Suppose a constraint is removed from this problem. Explain how this might affect each of the following:

(a) the feasible region.

(b) the optimal value of the objective function.

1. ________ diagrams are graphs of the data that are helpful in displaying the relationship between variables.

(a) relationship

(b) scatter

(c) utility

(d) decision tree

(e) binary

1. In regression models, the independent variable is also called the explanatory or predictor variable.

True

False

1. 23.  What are the main two purposes of regression analysis?

## 25.  Thesales manager of a large apartment rental complex feels the demand for apartments may be related to the number of newspaper ads placed during the previous month. She has collected the data shown in the accompanying table.

15                                                        6

9                                                        4

40                                                       16

20                                                         6

25                                                       13

25                                                         9

15                                                       10

35                                                       16

(a)   Find the regression analysis model.

(b)   If the number of ads is 30, we can estimate the number of apartments leased with the regression equation to be what?

(c)    Determine the SSR.

(d)   Determine the SST.

(e)    Determine the SSE.

1. 26.   Chrysler has developed a new minivan that has a startup cost of \$45,000,000. Each new van costs \$18,000 to make. If Chrysler plans to sell 3,750 minivans, what will be the selling price?
2. 27.  A toy manufacturer can manufacture only skateboards, only dolls, or some mixture of skateboards and dolls. Skateboards require five units of plastic and can be sold for a profit of \$1, while dolls require two units of plastic and can be sold for a \$.55 profit. Suppose that there are 360 person-minutes of labor available and that making one skateboard require 15 person-minutes and making one doll requires 18 person-minutes. If 60 units of plastic are available, what numbers of skateboards and/or dolls should be manufactured for the company to maximize profit?
1. Graph
2. Use corner point method

1. 28.   Assume the relationship of the number of telephones in service and population has historically

varied as follows:

Population             Number of phones

Year        (millions)                    (millions)

1                  130                               50

2                  140                               55

3                  150                               60

a. Determine the linear regression.

b. If in the fourth year the population is 170, what would be the predicted number of phones

(linear regression)?

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1. 29.   The ABC Company is considering the sale of a new product. There are \$1,750 of fixed costs

associated with the undertaking of this project. The product will sell for \$4 a unit, and the

variable costs are \$1.50. It is expected that 1,000 units will be sold.

a. What is the break-even point?

b. What is the expected profit?

30.   A construction company has a contract to complete a job in 180 days. It will have to pay

a penalty of \$10,000 per day for each day beyond 180 days that it takes to complete the project.

There is a some uncertainty about how long it will take due to weather conditions, possible

strikes, etc. Management has assigned a normal probability distribution to the number of days

necessary to complete the project. This distribution has a mean of 170 days and a standard

deviation of 12 days. What is the probability that the job will be completed on time?

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