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# 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.