MAT 540 WEEK 1 Homework-CH 1 and 11

MAT 540 WEEK 1 Homework-CH 1 and 11
Attached is
a template for you to use for Homework 1.
Note that I expect you to show the
work in your calculations and then insert your numerical answers in the yellow
boxes.

I will not
give you credit for your solutions (even partial credit) unless I can see your
work. As a worst case, you can do you work on paper, scan it and send the
scanned work plus the Excel template to me for grading.
Chapter 1,
Problems 2, 4, 12, 14, 20, 22
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,
Problems 18, 20, 26, 28, 30
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.