Quantitative Methods Math 5401. 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? 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? 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: InvestmentEconomic Conditions 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? 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.
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