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# Price for a new product

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You are in the process of deciding on the price for a new product. The goal is to maximizethe profit. The alternatives are different possible prices from \$2 per unit to \$10 per unit. Themodel to be used is described below. Let:X = number of units produced and soldC(X) = total cost of producing X unitsP = price to be chargedNP = total net profit (to be maximized)Cost relationship: C(X) = 800 + 1.25XSales relationship: X = – 100 + 2000/PProfit relationship: NP = P.X  C(X)a. Comment on the model in terms of reasonableness of the relationships.b. Find an approximate solution to the model by trial and error (i.e., use several values ofprice between \$2 and \$10, and try to find to a price that gives a good profit. Use of MSExcel is highly recommended).c. Find the optimum price value by following these steps:? Summarize net profit function in terms of price? Compute the derivative of the net profit function with respect to the price? Set the result equal to zero and solve for the price.

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