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 = 24 − 0.2x  (for 0 ≤ x ≤ 120), the price function for cars sold in Europe is q = 14 − 0.1y (for 0 ≤ y ≤ 140), 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 z are the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is  C = 27 + 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) =

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