1) CBT has agreed to finance the needs of a stereo wholesaler for the next month. To complete the loan agreement, the wholesaler must estimate the cash on hand during the first 90 days of operation. Daily receipts are normally distributed with a mean of $50,000 and a standard deviation of $12,000. Disbursements are also normally distributed with a mean of $48,000 and a standard deviation of $3,000.
(a) Construct a computer simulation model to keep track of the cash flow during the first 90 days of operation. Assume that initially that there is $75,000 of cash on hand.
(b) Repeat the simulation model constructed in part (a) 50 times using a data table. Use the results in the data table to estimate the probability that a short term loan will be needed.
(c) Suppose that CBT has agreed to finance a short term loan if the probability a loan is needed is between 3% and 7%. How much initial cash on hand should the stereo wholesaler have?
2) Bob Smith recently completed his MBA and accepted a job with a computer company. To ensure that his retirement is comfortable, he intends to invest $3,000 of his salary into a tax shelter retirement fund at the end of each year. Bob is not certain what the rate of return is, but knows that it is normally distributed with a mean of 13% and a standard deviation of 2%. If Bob is 30 years old, how much money should he expect to have when he is 60?
(a) Develop a computer simulation model to determine how much will be in his retirement fund after 30 years.
(b) Use a data table to perform 200 runs of the simulation model developed in part (a).
(c) Compute the average amount the fund will be worth using the results from the 200 runs in the data table.
(d) Obtain a histogram for the 200 run results. Use at least 7 class intervals.
(e) Based on the simulation results in the data table, estimate the probability that the fund will be more than $750,000 and the probability that the fund will be more than $1,000,000.
3) Anna is considering investing $150,000 by dividing it into three investments. But she is not sure how much to put in each one. The first investment is known to follow a uniform distribution with a rate of return that varies from -2% to 10%. The second investment follows a normal distribution with an average rate of return of 12% and a standard deviation of 6%. The third investment has a constant return of 6%.
(a) Construct a computer model to simulate Anna's investments for a 20 year period. Assume that the balances are cumulative. Include as input parameters the amounts invested in each type of investment. Try your simulation model using $50,000 in each investment. The simulation should keep track of the combined balance.
(b) Use data table to repeat the simulation designed in part (a) 300 times and record the results.
4) A project has four activities A, B, C and D that must be performed sequentially. The probability distributions for the required to complete each activity are as follows.
Activity A Time required (weeks) 4 5 6 7
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Probability .25 .35 .30 .10
Activity B Time required (weeks) 2 3 4
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Probability .55 .20 .25
Activity C Time required (weeks) 6 7 8 9 10
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.20 .25 .25 .15 .15
Activity D Time required (weeks) 5 10
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Probability .55 .45
(a) Construct a computer simulation model to simulate the time required to complete the project
(b) Carry out 100 runs of the model to and calculate the following: the average completion time, the standard deviation, the best completion time, the worst completion time and the probability that the completion time will be greater than 20 weeks.
(c) Construct a histogram for the 100 completion times using five class intervals.