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?
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?
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 |
|
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.
