Question 8 Suppose that the total monthly cost of producing x units (0 SX S100) of a certain product consists of a fixed cost of 2000 dollars and a variable cost of x3 - 17.5x2 - 700x dollars. If the total monthly revenue R(x) = (2000 + 50x)x dollars when x units are produced and sold. Find the cost function C(x) and profit function P(x) when x units of the product are produced and sold in a month. Determine the production level x at which the profit per month is maximized. Find the maximum profit per month. [12 marks]