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 = 550 - 0.11 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 = 40000 + 8 Q.

                a. If the goal of War Games is to maximize profits, calculate the firm

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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