3. War Games, Inc. produces games that simulate historical battles. The market i

Question

3. War Games, Inc. produces games that simulate historical battles. The market is small but loyal and War Games is the largest manufacturer. The company is now thinking about introducing a new game in honor of the sixtieth anniversary of the outbreak of World War II. Based on historical data regarding sales, War Games management forecasts demand for this game to be P = 50 - 0.002 Q, where Q denotes unit sales per year and P denotes the price in dollars. The cost of manufacturing (based on royalty payments to the designer of the game and the cost of printing and distribution) is C = 140000 + 10 Q.

a. If the goal of War Games is to maximize profits, calculate the firm’s optimal output, price, and profits?
b. If instead, the company’s goal is to maximize sales revenues, what will the price, output, and profit be?

Explanation / Answer

We are looking to max profit Profit=PxQ-C Gi enn we know P and C formulas substituting gives Profit=(50-0.002Q)Q-(140,000+10Q) =50Q-.0002Q^2-140000-10Q =40Q-0.002Q^2 To maximise - take thedifferentiall therefore 40-2X0.002Q=0 therefore Q= 10,000 To work out rest just feed back into formulas P=50-0.002Q =30 C=140,000+10Q =240,000 Total revenue= PQ=30*10000=300000 Total profit =300,000-240,000=60,000

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