Quantitative Methods Math 540

1. The Retread Tire Company recaps tires. The fixed annualcost of the recapping operation is $65,000. The variable cost of recapping atire is $7.5. The company charges$25 to recap a tire.

a. For an annual volume of 15, 000 tire, determine the totalcost, total revenue, and profit.

b. Determine theannual break-even volume for the Retread Tire Company operation.

2. Evergreen Fertilizer Company produces fertilizer. Thecompany’s fixed monthly cost is $25,000, and its variable cost per pound offertilizer 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 theprice of its fertilizer from $0.45 per pound to $0.55 per pound, what effect willthe change have on the break-even volume?

4. If Evergreen Fertilizer Company increases its advertisingexpenditure by $10,000 per year, what effect will the increase have on thebreak-even volume computed in problem 2?

5. Annie McCoy, a student at Tech, plans to open a hot dogstand inside Tech’s football stadium during home games. There are 6 home gamesscheduled for the upcoming season. She must pay the Tech athletic department avendor’s fee of $3,000 for the season. Her stand and other equipment will costher $3,500 for the season. She estimates that each hot dog she sells will costher $0.40. she has talked to friends at other universities who sell hot dogs atgames. Based on their information and the athletic department’s forecast thateach game will sell out, she anticipates that she will sell approximately 1,500hot dogs during each game.

a. What price should she charge for a hot dog in order tobreak even?

b. What factors might occur during the season that wouldalter the volume sold and thus the break-even price Annie might charge?

6. The college ofbusiness at Kerouac University is planning to begin an online MBA program. Theinitial start-up cost for computing equipment, facilities, course developmentand staff recruitment and development is $400,000. The college plans to chargetuition of $20,000 per student per year. However, the university administrationwill charge the college $10,000 per student for the first 100 students enrolledeach year for administrative costs and its share of the tuition payments.

a. How many students does the college need to enroll in thefirst year to break-even?

b. If the college can enroll 80 students the first year, howmuch profit will it make?

c. The collegebelieves it can increase tuition to $25,000, but doing so would reduceenrollment to 50. Should the college consider doing this?

7. The following probabilities for grades in managementscience 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 alternativeinvestments, A and B, under two possible future sets of economic conditionsgood and poor. There is a .60 probability of good economic conditions occurringand a .40 probability of poor economic conditions occurring. The expected gainsand losses under each economic type of conditions are shown in the followingtable:

Investment

Economic 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 normallydistributed, 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 50pounds?

10. The poloDevelopment Firm is building a shopping center. It has informed renters thattheir rental spaces will be ready for occupancy in 18 months. If the expectedtime until the shopping center is completed is estimated to be 15 months, witha standard deviation of 5 months, what is the probability that the renters willnot be able to occupy in 18 months?

11. The manager of the local National Video Store sellsvideocassette recorders at discount prices. If the store does not have a videorecorder in stock when a customer wants to buy one, it will lose the salebecause the customer will purchase a recorder from one of the many localcompetitors. The problem is that the cost of renting warehouse space to keepenough recorders in inventory to meet all demand is excessively high. Themanager 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. Themanager has estimated that monthly demand for recorders is normallydistributed, with a mean of 175 recorders and a standard deviation of 55.Determine the number of recorders the manager should order each month to meet85% of customer demand.