Strayer MAT540 All Homework Assignments (excpt wk 8 assignment)
MAT540
Week 1 Homework
MAT540 Homework
Week 1
Page 1
of 3
MAT540
Week 1 Homework
Chapter 1
1. The Retread Tire Company recaps tires. The
fixed annual cost of the recapping operation is $65,000. The variable cost of
recapping a tire is $7.5. The company charges$25 to recap a tire.
a. For an annual volume of 15, 000 tire,
determine the total cost, total revenue, and profit.
b. Determine the annual break-even volume for
the Retread Tire Company operation.
2. Evergreen Fertilizer Company produces
fertilizer. The company’s fixed monthly cost is $25,000, and its variable cost
per pound of fertilizer is $0.20. Evergreen sells the fertilizer for $0.45 per
pound. Determine the monthly break-even volume for the company.
3. If Evergreen Fertilizer Company in problem
2 changes the price of its fertilizer from $0.45 per pound to $0.55 per pound,
what effect will the change have on the break-even volume?
4. If Evergreen Fertilizer Company increases
its advertising expenditure by $10,000 per year, what effect will the increase
have on the break-even volume computed in problem 2?
5. Annie McCoy, a student at Tech, plans to
open a hot dog stand inside Tech’s football stadium during home games. There
are 6 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 $3,500 for the season. She estimates that each
hot dog she sells will cost her $0.40. 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 1,500 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?
6. The college of business at Kerouac
University 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 $400,000. The college plans to charge tuition of
$20,000 per student per year. However, the university administration will
charge the college $10,000 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 80 students the
first year, how much profit will it make?
MAT540
Homework
Week 1
Page 2
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c. The college believes it can increase
tuition to $25,000, but doing so would reduce enrollment to 50. Should the
college consider doing this?
Chapter 11
7. The following probabilities for grades in
management science have been determined based on past records:
Grade |
Probability |
A |
0.1 |
B |
0.2 |
C |
0.4 |
D |
0.2 |
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.
8. 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 |
$380,000 |
-$100,000 |
|
B |
$130,000 |
$85,000 |
|
Using the expected value of each investment
alternative, determine which should be selected.
9. The weight of the bags of fertilizer is
normally distributed, with a mean of 45 pounds and a standard deviation of 5
pounds. What is the probability that a bag of fertilizer will weigh between 38
and 50 pounds?
MAT540
Homework
Week 1
Page 3
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10. The polo Development Firm is building a
shopping center. It has informed renters that their rental spaces will be ready
for occupancy in 18 months. If the expected time until the shopping center is
completed is estimated to be 15 months, with a standard deviation of 5 months,
what is the probability that the renters will not be able to occupy in 18
months?
11. 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 85% 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 175 recorders and a standard deviation of 55.
Determine the number of recorders the manager should order each month to meet
85% of customer demand.
MAT540
Week 2 Homework
MAT540
Homework
Week 2
Page 1
of 4
MAT540
Week 2 Homework
Chapter 12
1. A local real estate investor in Orlando is
considering three alternative investments; a motel, a restaurant, or a theater.
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:
Weather Conditions |
|||||
Investment |
|||||
Shortage |
Stable Supply |
Surplus |
|||
Motel |
$-7,500 |
$12,000 |
$23,000 |
||
Restaurant |
3000 |
7,000 |
6,500 |
||
Theater |
5000 |
6,000 |
4,000 |
||
Determine the best investment, using the following
decision criteria.
a. Maximax
b. Maximin
c. Minimax regret
e. Equal likelihood
2. 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 35% chance of rain, a 25% chance of overcast skies,
and a 40% chance of sunshine, according to the weather forecast in college
junction, where the game is to be held. The manager estimates that the
following profits will result from each decision, given each set of weather
conditions:
MAT540
Homework
Week 2
Page 2
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Weather Conditions |
|||||
Decision |
|||||
Rain |
Overcast |
Sunshine |
|||
0.35 |
0.25 |
0.40 |
|||
Sun visors |
$-400 |
$-200 |
$1,500 |
||
Umbrellas |
2,100 |
0 |
-800 |
||
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.
3. Place-Plus, a real estate development firm,
is considering several alternative development projects. These include building
and leasing an office park, purchasing a parcel of land and building an office
building to rent, buying and leasing a warehouse, building a strip mall, 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 in the following payoff table.
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
0.45probability that interest rates will
decline, a 0.35 probability that rates will remain stable, and a
0.2 probability that rates will increase.
a. Using expected value, determine the best
project.
b. Determine the expected value of perfect
information.
Interest Rate |
|||||
Project |
|||||
Decline |
Stable |
Increase |
|||
Office park |
$0.4 |
$1.55 |
$3.5 |
||
Office building |
2.5 |
1.8 |
2.75 |
||
Warehouse |
1.7 |
1.45 |
1.5 |
||
Mall |
0.8 |
2.3 |
3.5 |
||
Condominiums |
3.2 |
1.5 |
0.5 |
||
MAT540
Homework
Week 2
Page 3
of 4
4. The director of career advising at Orange
Community College wants to use decision analysis to provide information to help
students decide which 2-year degree program they should pursue. The director
has set up the following payoff table for six of the most popular and
successful degree programs at OCC that shows the estimated 5-Year gross income ($)
from each degree for four future economic conditions:
Economic Conditions |
||||||
Degree Program |
||||||
Recession |
Average |
Good |
Robust |
|||
Graphic design |
150,000 |
175,000 |
220,000 |
200,000 |
||
Nursing |
160,000 |
180,000 |
205,000 |
215,000 |
||
Real estate |
125,000 |
165,000 |
220,000 |
210,000 |
||
Medical technology |
135,000 |
180,000 |
210,000 |
270,000 |
||
Culinary technology |
110,000 |
145,000 |
235,000 |
205,000 |
||
Computer information |
130,000 |
150,000 |
190,000 |
245,000 |
||
technology |
||||||
Determine the best degree program in terms of
projected income, using the following decision criteria:
a. Maximax
b. Maximin
c. Equal likelihood
5. Construct a decision tree for the following
decision situation and indicate the best decision.
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:
MAT540
Homework
Week 2
Page 4
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Gasoline
Availability
Dealership |
Shortage |
Surplus |
|||
0.7 |
0.3 |
||||
Compact cars |
$25,000 |
$150,000 |
|||
Full-sized cars |
-90,000 |
650,000 |
|||
Trucks |
125,000 |
170,000 |
|||
Decision Tree diagram to complete: |
|||||
Shortage 0.7 |
|||||
2 |
|||||
Compact cars |
Surplus 0.3 |
||||
Shortage 0.7 |
|||||
1 |
Full-sized cars |
3 |
|||
Surplus 0.3 |
|||||
Trucks |
Shortage 0.7 |
||||
4 |
|||||
Surplus 0.3 |
$250,000
$150,00
-$90,000
$650,000
$125,000
$170,000
MAT540
Week 3 Homework
MAT540
Homework
Week 3
Page 1
of 3
MAT540
Week 3 Homework
Chapter 14
1. The Hoylake Rescue Squad receives an
emergency call every 1, 2, 3, 4, 5, or 6 hours, according to the following
probability distribution. The squad is on duty 24 hours per day, 7 days per
week:
Time
Between
Emergency Calls (hr.) |
Probability |
||
1 |
0.15 |
||
2 |
0.10 |
||
3 |
0.20 |
||
4 |
0.25 |
||
5 |
0.20 |
||
6 |
0.10 |
||
1.00 |
|||
a. Simulate the emergency calls for 3 days
(note that this will require a “running” , or cumulative, hourly clock), using
the random number table.
b. Compute the average time between calls and
compare this value with the expected value of the time between calls from the
probability distribution. Why are the result different?
2. The time between arrivals of cars at the
Petroco Services Station is defined by the following probability distribution:
Time
Between
Emergency Calls (hr.) |
Probability |
||
1 |
0.35 |
||
2 |
0.25 |
||
3 |
0.20 |
||
4 |
0.20 |
||
1.00 |
|||
MAT540
Homework
Week 3
Page 2
of 3
a. Simulate the arrival of cars at the service
station for 20 arrivals and compute the average time between arrivals.
b. Simulate the arrival of cars at the service
station for 1 hour, using a different stream of random numbers from those used
in (a) and compute the average time between arrivals.</
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