1400PS4F23_Exercise

C OMPUTER P ROBLEM -S OLVING IN EGR 1400 E NGINEERING AND C OMPUTER S CIENCE F ALL 2023 P ROBLEM -S OLVING E XERCISE #4 S IMULATION 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: P T = nP v Where P T is the total profit, n is the number of vehicles sold and P v is the profit per vehicle. P ART A 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 v follows a normal distribution with a mean of $5250 and a standard deviation of $1100 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 we figured that we ’d give you a break ☺ . i.) What are the ranges for the 10 bins? ii.) Fill in the table below: Parameter Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5 n 8 5 9 2 8 P v $3300 $4725 $4500 $7250 $5725 P T Bin # $ Range iii.) Fill in the frequency of occurrences of each bin: 1: 2: 3: 4: 5: 6: 7: 8: 9: 10:

P ART B Write the following three methods and include in the Part D code listing : public int GetRandomUniform(int min, int max) This method returns a random number from a uniform distribution between min and max . public double GetRandomNormal(double mean, double stddev) This method returns a random number from a normal distribution with a mean of mean and standard deviation of stddev public int GetBinIndex(double mini, double maxi, int numbins, double valuetobin) This method returns the Bin Index given an input minimum of mini , input maximum of maxi , numbins number of bins, and a value to bin of valuetobin P ART C Include the methods created in part B to develop a Visual C# .NET program that will simulate the basic profit calculation, P T = nP v , where n follows a uniform distribution, P v follows a normal distribution, and the user can input the number of bins and number of iterations. The user must also input the min and max for n and the mean and standard deviation for P v . Finally, the user can click a button and the results will be graphed on a bar chart using the Microsoft Chart Control and the average total profit (P T ) will be displayed in a textbox. Turn in a screen shot of the resulting chart using: 1. Iterations: 10000 Bins: 5 n-min : 1 n-max : 10 P v -mean : 7725 P v -stddev : 2100 2. Iterations: 10000 Bins: 10 n-min : 1 n-max : 10 P v -mean : 7725 P v -stddev : 2100 3. Iterations: 10000 Bins: 10 n-min : 1 n-max : 10 P v -mean : 8000 P v -stddev : 2250 That’s three screen shots. P ART D Extend the Visual C# .NET program developed in part C to simulate the basic profit calculation, P T = nP v , where the user can select either a uniform or normal distribution for n using radio buttons and then must input the appropriate parameters ( min and max if they select uniform, mean and standard deviation if they select normal) and they can similarly select either a uniform or normal distribution for P v with appropriate parameters depending on the selection. Of course, the user will input the number of bins and number of iterations. Finally, the user can click a button and the results will be graphed on a bar chart using the Microsoft Chart Control and the average total profit (P T ) will be displayed in a textbox. Also include in the program any necessary input validation for all input values. Turn in a listing of the code and a screen shot of the resulting chart using: 1. Iterations: 10000 Bins: 5 n-min : 6 n-max : 11 P v -mean : 6125 P v -stddev : 1150 2. Iterations: 10000 Bins: 10 n-mean : 9 n-stddev : 2 P v -min : 1000 P v -max : 6000 3. Iterations: 10000 Bins: 10 n- mean : 12 n- stddev : 2 P v -min : 2300 P v -max : 5850 That’s three screen shots and a listing of the code for Parts B and D.