## management scince moudle

management scince moudle

For each problem, run Crystal Ball to generate random data. Write your answers in the appropriate places below. Submit your spreadsheet to the drop box and hand in this worksheet to me by Saturday March 7, 2015. If I am not in my office, you may slide it under my door or submit a scanned copy through the drop box.

1. A regional airline uses a 20-seat aircraft for a flight between Scranton and Pittsburgh. The demand for this flight is binomial with n = 20, and p = 0.9. Tickets sell for $150. Expenses for this flight include the pilot’s salary, fuel and maintenance. Previous financial records show that the minimum expense per flight is $1000, the most likely expense is $1500 and the maximum expense is $3000.

a) Find the expected profit per flight.

b) What is the standard deviation?

c) Find the probability that the flight will lose money.

2. A life insurance company sells a policy which pays $100,000 in case of death. The policy also pays hospital bills in case of injury. These bills average $50,000 with a standard deviation of $10,000. In any particular month there is a 5% chance of a death claim. The distribution of the number of injury claims per month is listed below:

Number of Claims 0 1 2 3 4 5 6

Probability .14 .27 .27 .18 .09 .04 .01

The company wants to estimate the total dollar amount of claims paid out each month to determine the minimum insurance premium it must charge customers to remain profitable.

Run 5000 simulations and answer the following questions:

a. Find the expected total claims paid out per month.

b. Find the standard deviation of claims paid per month

c. What is the probability that the amount of claims exceed $200,000 in any month?

d. What is the probability the claims exceed $300,000 in any month?

3. You sell fruit in the marketplace. You can buy apples wholesale for 50 cents each if you buy in multiples of 10. You can sell individual apples for 75 cents each. If the apples don’t sell that day, you must discard them. Your daily demand averages 37 apples and follows a Poisson distribution. Should you buy 30 apples or 40 apples? Run 1000 simulations for each scenario and complete the following table:

Buy 30 Apples Buy 40 Apples

Expected Profit:

Standard Deviation

Probability that you lose money

What is your decision? Justify your answer.