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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

    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

    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

    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.