Suppose that a real estate agent earns a basic salary of $90,000 per month, plus some commission and bonuses. Suppose that she receives a commission of 10% of sales. Bonuses are a lumpsum amount of 1335,0013 if her monthly sales exceed $500,000 and a further lumpsum of $50,000 if her monthly sales exceed $1,000,000. a. Find the function that relates monthly sales to the total monthly pay of this real estate agent. Let S be monthly sales and P' be the real estate agents pay. b. Graph the pay function, P(S), and appropriately label the relevant lines and points. C. Is 13(3) continuous? If not, at which point{s) is PCS) discontinuous and why? d. Is the function differentiable everywhere? Why or why not? e. What do the properties of P6") imply about the incentives {to sell real estate) created by such