# Profit Maximization Problem

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1)The manufacturer of high-quality flatbed scanners is trying to decide what price to set for itsproduct. The costs of production and the demand for the product are assumed to be as follows: TC = 500,000 + 0.85Q + 0.015 Q2Q = 14.166 – 16.6Pa)Determine the short-run profit-maximizing price.b)Plot this information on a graph showing AC, AVC, MC, P and MR2)An amusement park, whose customer set is made up of two markets, adults and children, hasdeveloped demand schedules as follows: QuantityPrice (\$)AdultsChildren51520614187131681214911121010101198128613741462The marginal operating cost of each unit of quantity is \$5. (Hint: Because marginal cost is a constant,so is average cost. Ignore fixed cost). The owners of the amusement park want to maximize profits. a)Calculate the price, quantity, and profit if1.The amusement park charges a different price in each market2.The amusement park charges the same price in the two markets combined3.Explain the difference in the profit realized under the two situationsb)(Mathematical solution) The demand schedules presented in Problem 2 can be presented inequation form as follows (where subscript A refers to the adult market, subscript C refers tothe market for children, and subscript T to the two markets combined):QA = 20 – 1PAQC = 30 – 2PCQT = 50 – 3PTSolve these equations for the maximum profit that the amusement park will attain when itcharges different prices in the two markets and when it charges a single price for thecombined market.3)The Bramwell corporation has estimated its demand function and total cost function to be asfollows: Q = 25 – 0.05P

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