申論題

6. (10%) In February 2021, 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 = 20 - 0.2x (for 0 ≤ x ≤ 100), the price function for cars sold in Europe is q = 16 - 0.1y (for 0≤  y≤ 160), and the price function for cars sold in Asia is r = 12 - 0.1z (for 0 ≤ z ≤  120), 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 production cost function is C = 22 +4(x +y+z)thousand dollars.