3. priceBreak-even quantitiesEffectsQ12 250000.150.655,555.56
Stokes, Nicole: Stokes, Nicole:
The break even volume with reduce.-44444.44Fix Cost &
AdvertisingVariable Costsales priceBreak-even
quantitiesEffectsQ14 390000.220.6-55555.56Fix Cost (vender's
fee & equipment)Variable Costsales priceBreak-even
quantitiesQ20 - A75000.352000Fix Cost (vender's fee &
equipment)Variable Costsales priceBreak-even
quantitiesNoteQ20 - B75000.352000Fix Cost Variable Costsales
priceBreak-even quantitiesQ22 - A3500001200018000Fix
CostVariable Costsales volumesale PriceProfitQ22 -
B350000120007518000Fix CostVariable Costsales volumesale
PriceProfitNoteQ22 - C350000120003524000Please give your
answers in YELLOW boxes
Chapter_11Q18GradeScaleProbabilityA40.1B30.3C20.4D10.1F0
0.11Expected GradeCourse VarianceQ20Economic
ConditionsInvestmentGoodPoorProbability0.60.4A$900,000($80
0,000)B120,00070,000Choose investment A or
B?Q26DistributionMeanStandard deviationLower weight
limitUpper weight
LimitProbabilityNormal5064555Q28DistributionMeanStandard
deviationOccupiedProbability NOT
occupiedNormal14419Q30DistributionMeanStandard
deviationProbabilityNumber of recorders
orderedNormal180600.9
MAT540 Homework
Week 2
Page 1 of 3
MAT540
Week 2 Homework
Chapter 12
8. A local real estate investor in Orlando is considering three
alternative investments: a motel, a restaurant, or a theater.
4. Profits from the motel or restaurant will be affected by the
availability of gasoline and the number of tourists; profits from
the theater will be relatively stable under any conditions. The
following payoff table shows the profit or loss that could result
from each investment:
Gasoline Availability
Investment
Shortage
Stable Supply
Surplus
Motel
$-8,000
$15,000
$20,000
Restaurant
2,000
8,000
6,000
Theater
6,000
6,000
5,000
Determine the best investment, using the following decision
criteria.
a. Maximax
b. Maximin
c. Minimax regret
d. Hurwicz (α = 0.4)
e. Equal likelihood
16. A concessions manager at the Tech versus A&M football
game must decide whether to have the vendors sell sun visors or
umbrellas. There is a 30% chance of rain, a 15% chance of
overcast skies, and a 55% chance of sunshine, according to the
weather forecast in College Junction, where the game is to be
5. held. The manager estimates that the following profits will
result from each decision, given each set of weather conditions:
Weather Conditions
Decision
Rain
Overcast
Sunshine
.30
.15
.55
Sun visors
$-500
$-200
$1,500
Umbrellas
2,000
0
-900
a. Compute the expected value for each decision and select the
best one.
b. Develop the opportunity loss table and compute the expected
opportunity loss for each decision.
24. In Problem 13 the Place-Plus real estate development firm
has hired an economist to assign a probability to each direction
interest rates may take over the next 5 years. The economist has
determined that there is a .50 probability that interest rates will
decline, a .40 probability that rates will remain stable, and a .10
probability that rates will increase.
a. Using expected value, determine the best project.
b. Determine the expected value of perfect information.
Reference Problem 13: Place-Plus, a real estate development
firm, is considering several alternative development projects.
These include building and leasing an office park, purchasing a
6. parcel of land and building an office building to rent, buying
and leasing a warehouse, building a strip mall, and building and
selling condominiums. The financial success of these projects
depends on interest rate movement in the next 5 years. The
various development projects and their 5-year financial return
(in $1,000,000s) given that interest rates will decline, remain
stable, or increase, are shown in the following payoff table:
Interest Rate
Project
Decline
Stable
Increase
Office park
$0.5
$1.7
$4.5
Office building
1.5
1.9
2.5
Warehouse
1.7
1.4
1.0
Mall
0.7
2.4
3.6
Condominiums
3.2
1.5
0.6
7. 32. The director of career advising at Orange Community
College wants to use decision analysis to provide information to
help students decide which 2-year degree program they should
pursue. The director has set up the following payoff table for
six of the most popular and successful degree programs at OCC
that shows the estimated 5-year gross income ($) from each
degree for four future economic conditions:
Economic Conditions
Degree Program
Recession
Average
Good
Robust
Graphic design
145,000
175,000
220,000
260,000
Nursing
150,000
180,000
205,000
215,000
Real estate
115,000
165,000
220,000
320,000
Medical technology
130,000
180,000
210,000
280,000
Culinary technology
115,000
8. 145,000
235,000
305,000
Computer information technology
125,000
150,000
190,000
250,000
Determine the best degree program in terms of projected
income, using the following decision criteria:
a. Maximax
b. Maximin
c. Equal likelihood
d. Hurwicz (α = 0.50)
36. Construct a decision tree for the decision situation
described in Problem 25 and indicate the best decision.
Reference Problem 25: Fenton and Farrah Friendly, husband-
and-wife car dealers, are soon going to open a new dealership.
They have three offers: from a foreign compact car company,
from a U.S. producer of full-sized cars, and from a truck
company. The success of each type of dealership will depend on
how much gasoline is going to be available during the next few
years. The profit from each type of dealership, given the
availability of gas, is shown in the following payoff table:
Gasoline Availability
Dealership
Shortage
Surplus
.6
.4
Compact cars
$ 300,000
$150,000
9. Full-sized cars
-100,000
600,000
Trucks
120,000
170,000
Decision Tree diagram to complete:
MAT540 Homework
Week 3
Page 3 of 3
MAT540
Week 1 Homework
Chapter 1
2. The Retread Tire Company recaps tires. The fixed annual
cost of the recapping operation is $60,000.The variable cost of
recapping a tire is $9.The company charges $25 to recap a tire.
a. For an annual volume of 12,000 tires, determine the total
cost, total revenue, and profit.
b. Determine the annual break-even volume for the Retread Tire
Company operation.
4. Evergreen Fertilizer Company produces fertilizer. The
company’s fixed monthly cost is $25,000, and its variable cost
per pound of fertilizer is $0.15. Evergreen sells the fertilizer for
$0.40 per pound. Determine the monthly break-even volume for
the company.
12. If Evergreen Fertilizer Company in Problem 4 changes the
price of its fertilizer from $0.40 per pound to $0.60 per pound,
what effect will the change have on the break-even volume?
14. If Evergreen Fertilizer Company increases its advertising
expenditures by $14,000 per year, what effect will the increase
have on the break-even volume computed in Problem 13?
10. Reference Problem 13: If Evergreen Fertilizer Company
changes its production process to add a weed killer to the
fertilizer in order to increase sales, the variable cost per pound
will increase from $0.15 to $0.22. What effect will this change
have on the break-even volume computed in Problem 12?
20. Annie McCoy, 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 $0.35. 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 anticipates that she will sell
approximately 2,000 hot dogs during each game.
a. What price should she charge for a hot dog in order to break
even?
b. What factors might occur during the season that would alter
the volume sold and thus the break-even price Annie might
charge?
22. The College of Business at Tech is planning to begin an
online MBA program. The initial start-up cost for computing
equipment, facilities, course development, and staff recruitment
and development is $350,000.The college plans to charge tuition
of $18,000 per student per year. However, the university
administration will charge the college $12,000 per student for
the first 100 students enrolled each year for administrative costs
and its share of the tuition payments.
a. How many students does the college need to enroll in the first
year to break even?
b. If the college can enroll 75 students the first year, how much
profit will it make?
c. The college believes it can increase tuition to $24,000, but
doing so would reduce enrollment to 35. Should the college
consider doing this?
11. Chapter 11
18. The following probabilities for grades in management
science have been determined based on past records:
Grade
Probability
A
0.10
B
0.30
C
0.40
D
0.10
F
0.10
1.00
The grades are assigned on a 4.0 scale, where an A is a 4.0, a B
a 3.0, and so on. Determine the expected grade and variance for
the course.
20. An investment firm is considering two alternative
investments, A and B, under two possible future sets of
economic conditions, good and poor. There is a .60 probability
of good economic conditions occurring and a .40 probability of
poor economic conditions occurring. The expected gains and
losses under each economic type of conditions are shown in the
following table:
Economic Conditions
Investment
Good
Poor
A
$900,000
-$800,000
12. B
120,000
70,000
Using the expected value of each investment alternative,
determine which should be selected.
26. The weight of bags of fertilizer is normally distributed,
with a mean of 50 pounds and a standard deviation of 6 pounds.
What is the probability that a bag of fertilizer will weigh
between 45 and 55 pounds?
28. The Polo Development Firm is building a shopping center.
It has informed renters that their rental spaces will be ready for
occupancy in 19 months. If the expected time until the
shopping center is completed is estimated to be 14 months, with
a standard deviation of 4 months, what is the probability that
the renters will not be able to occupy in 19 months?
30. The manager of the local National Video Store sells
videocassette recorders at discount prices. If the store does not
have a video recorder in stock when a customer wants to buy
one, it will lose the sale because the customer will purchase a
recorder from one of the many local competitors. The problem
is that the cost of renting warehouse space to keep enough
recorders in inventory to meet all demand is excessively high.
The manager has determined that if 90% of customer demand
for recorders can be met, then the combined cost of lost sales
and inventory will be minimized. The manager has estimated
that monthly demand for recorders is normally distributed, with
a mean of 180 recorders and a standard deviation of 60.
Determine the number of recorders the manager should order
each month to meet 90% of customer demand.
