# Calculating break-even points and developing linear regressions

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1. There is a fixed cost of $50,000 to start a production process. Once the process has

begun, the variable cost per unit is $25. The revenue per unit is projected to be $45. Find

the break-even point.

2. Administrators at a university are planning to offer a summer seminar. It costs $3000

to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per

student for the administrators to provide the course materials. If we know that 20 people

will attend, what price should be charged per person to break even?

3. An automotive center keeps track of customer complaints received each week. The

probability distribution for complaints can be represented as a table, shown below. The

random variable xi represents the number of complaints, and p(xi) is the probability of

receiving xi complaints.

xi 0 1 2 3 4 5 6

p(xi) .10 .15 .18 .20 .20 .10 .07

a. What is the probability that they receive less than 3 complaints in a week?

b. What is the average number of complaints received per week?

4. A loaf of bread is normally distributed with a mean of 22 ounces and a standard

deviation of 0.5 ounces. What is the probability that a loaf is larger than 21 ounces?

5. The local operations manager for the IRS must decide whether to hire 1, 2, or 3

temporary workers. He estimates that net revenues will vary with how well taxpayers

comply with the new tax code. The probabilities of low, medium and high compliance

are 0.3, 0.4, and 0.3, respectively, and the payoff table is shown below. Using expected

values, determine how many workers the company should hire.

# of Low Medium High

workers compliance compliance compliance

1 50 50 50

2 20 60 100

3 -10 70 150

6. The number of cars arriving at Joe Kelly’s oil change and tune-up place during the last

200 hours of operation is observed to be the following.

Number of Frequency

cars arriving

4 10

5 30

6 70

7 50

8 40

1

a. Determine the probability distribution, and the cumulative probability distribution of

car arrivals.

b. Simulate 20 hours of car arrivals at Joe Kelly’s oil change and tune-up place.

c. For the simulation in (b), what is the average number of cars arriving per hour?

7. Given the following data on hotel check-ins for a 6-month period:

Month Number of rooms

July 70

August 105

September 90

October 120

November 110

December 115

a. What is the 3-month moving average for January?

b. What is the 5-month moving average for January?

8. Recent actual and forecasted data for product XYZ is given in the following table.

Determine the MSE, MAD, cumulative error and average error.

Month Actual

Demand

February 20

March 22

April 33

May 35

June 31

July 48

August 41

September -

9. The following table summarizes data between money spent on gambling and winnings

for Robert.

Money Spent Money Won

x y

12 62

10 54

16 86

18 100

2

15 80

10 57

5 26

12 60

22 105

25 140

Develop a linear regression equation for these data and forecast how much money Robert

will win if he spends $30.

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#### Solution Summary

Calculations are made to explain for multiple questions how to calculate break even points and form linear regressions.