# Operation Research homework

1.Demello publishing is trying to decide if it should produce and market a new novel. Fixed costs for the novel are estimated at \$10,000. Variable cost is estimated at either one dollar or two dollars with each price equally likely. The selling price is seven dollars and demand is expected to follow a normal distribution with me in 2500 with A standard deviation of 500.

A) Carry out a simulation use 100 trials.

B) obtain a set of summary statistics

2.CBT has agreed to finance the needs of the 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 Ameena \$50,000 and a standard deviation of \$12,000. Disbursements are also normally distributed was a mean of \$40,000 and a standard deviation of \$3000

A) construct a computer stimulation 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 the CBT has agreed to finance a short-term loan if the probability a loan is needed is between 2% and 7%. How much initial cash on hand to the stereo wholesaler have?

3.Bob Smith recently completed his MBA and excepted a job with the computer company. To ensure that his retirement is comfortable he intends to invest \$3000 of the salary into tax shelter retirement fund at the end of each year. That is us are going at 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 would 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 fun 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 stimulation results in the data table, estimate the probability that the funnel be more than \$750,000 in the probability that the phone will be more than \$1 million.

4.Anna is considering investing \$150,000 by dividing it into three investments. But she’s not sure how much to put in each one. The first investment is known to follow a uniform distribution with the 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 on his investments for a 20 year period assume that the balances are cumulative. Include as input para meters the mounds invested in each type of investment. Cheyer simulation model using \$50,000 in each investment. The simulation table she keep track of the combined balance.

B) use a data table to repeat the simulation designing part a 300 times and record results.

C) determine the best and worst case, range, mean, and standard deviation for the data.

D) construct a histogram for the output data.

E) try your simulation model using \$75,000 in investment 1, \$50,000 investment 2, and \$25,000 in investment 3.

5.Cable time Inc. Produces telecommunication cable from five components. A single wire forms the center conductor, oblivion mesh wire forms the outer conductor, two types of plastic tubing for inner and outer insulation, and a plastic tube for additional insulation. Orders have been placed for each component in quantities of 1000 feet. Based on historical Data it is known that the supplier has delivered the order to mount with uniform variation reinjuring as follows. Center conductor, 1000 +- 10 feet; mesh wire, 1,000 +- 5 feet; inner insulation, 1,000 +- 20 feet; outer insulation, 1,000 +- 20 feet, the outside tube, 1,000+-25 feet.

A)construct a computer simulation model to simulate The length of cable produced.

B)Carry out 200 runs of the simulation and determine the following: the average cable length, the standard deviation, the best wire length, the worst wire length and the probability that the wire length will be greater than 995 feet.

C) use the data from Part (b) and construct a histogram. Is the distribution bell shaped?
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