Can you please answer Problem 5 and provide a detailed answer/explanation (Subject: Stochastic Operations Research)

Please submit your work via Blackboard: 1. A single pdf file includes the following: a. Main results and discussions b. For part (a) of problems 1 4, please list all the simulation output using CFRN 2. An excel file contains your simulations Definition: Chen's Favorite Random Numbers (CFRN) : {0.025,0.075,0.125,0.175,, 0.875,0.925,0.975}. There are 20 numbers in this set. Obviously, these are not good random numbers. However, we will use these numbers several times in our assignments. For your convenience, there is an Excel file containing CFRN available at Blackboard. 5. (45 points) Imagine you are the manager for a firm that is planning to introduce a new product. We need to determine the selling price for this new product. The first year net profit from this product depends on: - Selling price per unit ($100P$200). This is what you need to determine. - Fixed costs (for overhead, advertising, etc.) This is assumed to be $100. - Sales volume (S) in units can cover quite a range. When we lower the selling price, the sales volume will increase. Suppose that S Uniform(201-P, 402-2P). - Unit cost varies depending on multiple factors such as production experience, raw material costs, and the sales volume. When the sales volume increases, the unit cost decreases as we produce more. Assume the Unit Cost Uniform (100,200+1000/S). Net profit is calculated as Net Profit =S(P Unit cost ) Fixed costs. Conduct an extensive Monte Carlo simulation to estimate the expected net profit. (a) If we decide that P=$110, what is the expected net profit? (b) If we decide that P=$120, what is the expected net profit? (c) What is a good choice of P? You have to conduct more simulation to support your recommendation. For ease of analysis, you can assume that running 200 simulation replications is sufficient to give you a good estimate. Please submit your work via Blackboard: 1. A single pdf file includes the following: a. Main results and discussions b. For part (a) of problems 1 4, please list all the simulation output using CFRN 2. An excel file contains your simulations Definition: Chen's Favorite Random Numbers (CFRN) : {0.025,0.075,0.125,0.175,, 0.875,0.925,0.975}. There are 20 numbers in this set. Obviously, these are not good random numbers. However, we will use these numbers several times in our assignments. For your convenience, there is an Excel file containing CFRN available at Blackboard. 5. (45 points) Imagine you are the manager for a firm that is planning to introduce a new product. We need to determine the selling price for this new product. The first year net profit from this product depends on: - Selling price per unit ($100P$200). This is what you need to determine. - Fixed costs (for overhead, advertising, etc.) This is assumed to be $100. - Sales volume (S) in units can cover quite a range. When we lower the selling price, the sales volume will increase. Suppose that S Uniform(201-P, 402-2P). - Unit cost varies depending on multiple factors such as production experience, raw material costs, and the sales volume. When the sales volume increases, the unit cost decreases as we produce more. Assume the Unit Cost Uniform (100,200+1000/S). Net profit is calculated as Net Profit =S(P Unit cost ) Fixed costs. Conduct an extensive Monte Carlo simulation to estimate the expected net profit. (a) If we decide that P=$110, what is the expected net profit? (b) If we decide that P=$120, what is the expected net profit? (c) What is a good choice of P? You have to conduct more simulation to support your recommendation. For ease of analysis, you can assume that running 200 simulation replications is sufficient to give you a good estimate