# Quantities Methods in Business

Question 4:

The 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.

Question 12:

If the 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?

Question 18:

The General Store at State University is an auxiliary bookstore located near the dormitories sells academic supplies, toiletries, sweatshirts and T-shirts, magazines, packaged food items, canned soft drinks and fruit drinks. The manager of the store has noticed that several pizza deli services near campus make frequent deliveries. As such, the manager is considering selling pi the store. She could buy premade frozen pizzas and heat them in an oven. The cost of the oven freezer would be $27,000. The frozen pizzas cost $3.75 each to buy from a distributor and to pare (including labor and a box). To be competitive with the local delivery services, the man: believes she should sell the pizzas for $8.95 apiece. The manager needs to write up a propos the university's director of auxiliary services.

a. Determine how many pizzas would have to be sold to break even.

b. If the General Store sells 20 pizzas per day, how many days would it take to break even?

c. The manager of the store anticipates that once the local pizza delivery services start losing business they will react by cutting prices. If after a month (30 days) the manager has to lower the price of a pizza to $7.95 to keep demand at 20 pizzas per day, as she expects, what will the new break-even point be, and how long will it take the store to break even?

Question 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 condi¬tions' occurring and a .40 probability of poor economic conditions' occurring. The expected gains and losses under each economic condition are shown in the following table. Using the expected value of each investment alternative, determine which should be selected.

Economic Conditions

Investment Good Poor

A $900,000 -$800,000

B 120,000 70,000

Question 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 proba¬bility that the renters will not be able to move in 19 months?

Question 8:

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 shown the profit or loss that could result from each investment.

Gasoline Availability

Investment Shortage Stable Supply Surplus

Motel $-8,000 $15,000 $20,000

Restuarant 2,000 8,000 6,000

Theater 6,000 6,000 5,000

Determine the best investment using the following decision criteria.

a. Maximax

b. Maximin

c. Minimax regret

d. Hurwicz ( α =.4)

e. Equal likelihood

Question 18:

The Miramar Company is going to introduce one of three new products: a widget, a hummer, or a nimnot. The market conditions (favorable, stable, or unfavorable) will determine the profit or loss the company realizes, as shown in the following payoff table.

Market Conditions

Favorable Stable Unfavorable

Product .2 .7 .1

Widget $120,000 $70,000 $-30,000

Hummer 60,000 40,000 30,000

Nimnot 35,000 30,000 30,000

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

product.

c. Determine how much the firm would be willing to pay to a market research firm to gain better information about future market conditions.

Question 28:

The manager of the greeting card section of mazey's department store is considering

her order for a particular line of Christmas Cards. The cost of each box of cards is $3; each box will be sold for $5 during the Christmas season. After Christmas, the cards will be sold for $2 a box. The card section ¬manager believes that all leftover cards can be sold at that price. The estimated demand during Christmas season for the line of Christmas cards, with associated probabilities, is shown as follows:

Demand (boxes) Probability

25 .10

26 .15

27 .30

28 .20

29 .15

30 .10

a. Develop the payoff table for this decision situation.

b. Compute the expected value for each alternative, and identify the best decision.

c. Compute the expected value of perfect information.

Question 6:

Every time a machine breaks down at the Dynaco Manufacturing Company , either one, two, or three hours are required to fix it, according to the following probability distribution.

Repair Time (hr) Probability

1 .30

2 .50

3 .20

a. Simulate the repair time for 20 weeks, and then compute the average weekly repair time.

b. If the random numbers that are used to simulate breakdowns per week are also used to sim¬ulate repair time per breakdown, will the results be affected in any way? Explain.

c. If it costs $50 per hour to repair a machine when it breaks down (including lost productivity), determine the average weekly breakdown cost.

d. The Dynaco Company is considering a preventive maintenance program that would alter the probabilities of machine breakdowns per week as shown in the following table. The weekly cost of the preventive maintenance program is $150. Using simulation, determine whether or not the company should institute the preventive maintenance program.

Machine Breakdowns per Week Probability

0 .20

1 .30

2 .20

3 .15

4 .10

5 .05

1.00

Question 8:

The Bayside Foundation Hotel is adjacent to County Coliseum, a 24,000-seat arena that is home to the city's professional basketball and ice hockey teams, and that hosts a variety of concerts, trade shows, and conventions throughout the year. The hotel has experienced the following occupancy rates for the past nine years since the coliseum opened.

Year Occupancy Rate (%)

1 83

2 78

3 75

4 81

5 86

6 85

7 89

8 90

9 86

Compute an exponential smoothing forecast with α = .20, an adjusted exponential smoothing forecast with α = .20 and β = .20, and a linear trend line forecast. Compare the three forecasts using MAD and average error (E), and indicate which seems to be most accurate.

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