Question

As we've previously seen, equations describing situations often contain uncertain parameters, that is, parameters that aren't necessarily a single value but instead are associated with a probability distribution function. When more than one of the variables is unknown, the outcome is difficult to visualize. A common way to overcome this difficulty is to simulate the scenario many times and count the number of times different ranges of outcomes occur. One such popular simulation is called a Monte Carlo Simulation. In this problem-solving exercise you will develop a program that will perform a Monte Carlo simulation on a simple profit function. Consider the following total profit function: P1 =nP Where Pr is the total profit, nt is the number of vehicles sold and P, is the profit per vehicle. PARTA Compute 5 iterations of a Monte Carlo simulation given the following information: n follows a uniform distribution with minimum of 1 and maximum 10 P follows a normal distribution with a mean of S7000 and a standard deviation of $1750 Number of bins: 10 Recall that for all practical purposes we will use 3 std. deviations from the mean as the maximum value for parameters following a normal distribution. Obviously, 5 iterations are not very many. In fact, typically you would simulate 10,000 iterations or so to view meaningful results but I figured that I'd give you a break . If you'd like to compute 10,000 iterations by hand for extra credit, go ahead... ii.) What are the ranges for the 10 bins? Fill in the table below: Iteration 3 Iteration + Iteration 5 Parameter Iteration 1 Iteration 2 38 S3750 $4500 S7000 S6700 S7750 S Range

Answer 1

i)

If normal distribution is chosen with mean $7000 and standard deviation(sd) $1750 then the range is 7000-(3*1750) to 7000 + (3*1750) , which is (1750,12250)

Thus the range is 12250-1750 = 10500. since total number of bins is 10, the size of each bin is 10500/10=1050

Thus the ranges for the bins are

1750-2800,

2800-3850,

3850-4900,

4900-5950,

5950-7000,

7000-8050,

8050-9100,

9100-10150,

10150-11200,

11200-12250

ii)

Pt is obtained by multiplying Pv and n.

Based on the value of Pv it is classified into the bin # based on above bin mapping.

Range of Pv is the same for all iterations based on the above assumed distribution.

The table will be as follows

n	3	8	5	9	6
Pv	3750	4500	7000	6700	7750
Pt	11250	36000	35000	60300	46500
Bin #	2	3	5	5	6
$ Range	10500	10500	10500	10500	10500