The marketing department of a company is planning to launch a new product. They need to estimate the first-year net profit from this product, which depends on several factors, including sales volume, selling price per unit, unit cost, and fixed costs. In particular, net profit can be calculated as Net profit = sales volume * (selling price - unit cost) fixed costs Fixed costs, including overhead, advertising, line installation, etc., are known to be $1,200,000. Based on the market analysis, the demand for the new product is modeled using three potential scenarios of high demand, medium demand, and low demand with probabilities 0.1, 0.6, and 0.3, respectively. Under a high-demand scenario, the company expects to sell q = 100,000-10*p-2*p2 units of the new product, where p is the selling price of the new product. Under a medium- and low-demand scenario, the company expects to sell q = 75,000-5*p-3*p? units and q = 50,000-p-5*p? units of the new product, respectively. To ensure economic feasibility and competitiveness of the new product, the marketing department is only considering a selling price range of $50 to $100. The unit cost for the new product involves uncertainty and the production manager has estimated the unit cost to be anywhere between $5 and $15 with a most likely value of $7. a) Use @RISK to develop a Monte Carlo simulation model to estimate the distribution of the net profit for the new product if the selling price is set at $50. Report the statistics for the net profit. Use 10,000 iterations. (10 points) b) Perform sensitivity analysis to identify the factor that has the highest impact on the net profit. (5 points) c) Use RISKOptimizer to identify the optimal selling price that maximizes the average of the net profit. (10 points) The marketing department of a company is planning to launch a new product. They need to estimate the first-year net profit from this product, which depends on several factors, including sales volume, selling price per unit, unit cost, and fixed costs. In particular, net profit can be calculated as Net profit = sales volume * (selling price - unit cost) fixed costs Fixed costs, including overhead, advertising, line installation, etc., are known to be $1,200,000. Based on the market analysis, the demand for the new product is modeled using three potential scenarios of high demand, medium demand, and low demand with probabilities 0.1, 0.6, and 0.3, respectively. Under a high-demand scenario, the company expects to sell q = 100,000-10*p-2*p2 units of the new product, where p is the selling price of the new product. Under a medium- and low-demand scenario, the company expects to sell q = 75,000-5*p-3*p? units and q = 50,000-p-5*p? units of the new product, respectively. To ensure economic feasibility and competitiveness of the new product, the marketing department is only considering a selling price range of $50 to $100. The unit cost for the new product involves uncertainty and the production manager has estimated the unit cost to be anywhere between $5 and $15 with a most likely value of $7. a) Use @RISK to develop a Monte Carlo simulation model to estimate the distribution of the net profit for the new product if the selling price is set at $50. Report the statistics for the net profit. Use 10,000 iterations. (10 points) b) Perform sensitivity analysis to identify the factor that has the highest impact on the net profit. (5 points) c) Use RISKOptimizer to identify the optimal selling price that maximizes the average of the net profit. (10 points)
