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1) CBT has agreed to finance the requirements of a stereo wholesaler for the next month. To complete loan agreement, the wholesaler should estimate cash on hand during first 90 days of operation. Daily receipts are usually distributed with the mean of $50,000 and a standard deviation of $12,000. Disbursements are also usually distributed with a mean of $48,000 and a standard deviation of $3,000.

(a) Construct a computer simulation model to keep track of cash flow during first 90 days of operation. Suppose that initially 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) Assume that CBT has agreed to finance a short term loan if the probability a loan is required is between 3% and 7%. How much initial cash on hand must the stereo wholesaler have?

2) Bob Smith recently completed his MBA and accepted a job with the computer company. To makesure that his retirement is comfortable, he intends to invest $3,000 of his salary into a tax shelter retirement fund at 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 must 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) find out the average amount the fund would 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
             Probability                       .25           .35             .30            .10

Activity B  Time required (weeks)      2             3            4
                     Probability                .55           .20          .25

Activity C      Time required (weeks)      6           7            8             9         10
                                                         .20         .25        .25         .15         .15

Activity D       Time required (weeks)       5            10                                                            
                           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 find out 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.

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  • Category:- Math
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