A local toy company manufactures and sells video games. The company has found that the demand equation is p = 3q + 190, and that the cost function is given by C(q) = 90q + 39. Here p is the prices in dollars, and q is the number of video games. Answer the following questions. (a) What is the revenue function? (b) What is the profit function? (c) What is the average rate of change of profit for selling between 10 and 15 video games? (d) What is the instantaneous rate of change of profit when q = 10? (e) What is the maximum profit that can be achieved?