(Solved): Submit Answel 6. [-/6 Points] PRACTICE ANOTHER An automobile manufacturer sells cars in America, Eur ...
Submit Answel 6. [-/6 Points] PRACTICE ANOTHER An automobile manufacturer sells cars in America, Europe, and Asia, charging a different price in each of the three markets. The price function for cars sold in America is
p=22-0.2x(for
0<=x<=110), the price function for cars sold in Europe is
q=15-0.1y(for
0<=y<=150), and the price function for cars sold in Asia is
r=19-0.1z(for
0<=z<=190), all in thousands of dollars, where
x,y, and
zare the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is
C=24+4(x+y+z)thousand dollars. (a) Find the company's profit function
P(x,y,z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]
P(x,y,z)=
◻(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials
P_(x^('))P_(y^(')), and
P_(z)equal to zero and solve. Assuming that the maximum exists, it must occur at this point.] America
◻Europe
◻Asia
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