1. A small company manufactures and sells lamps. The production manager has determined that the cost and demand functions for x lamps per week are Cost: C(33) = 100 + 202360315" Demand: 13:4080le a. Find an equation for the profit function 13(3)), which gives the profit of selling :1: lamps. b. Find the marginal profit function. c. Find the Critical numbers of P (x) d. How many lamps must be sold in order to maximize profit? e. Find the maximum profit. 2. The number of homes with access to internet via cable television between 1998 and 2005 can be modeled by the equation f (11:) = 138.27 -|- 76.29 111(m), where f (a?) is measured in millions of homes a: years after 1990. a. Find and interpret f(12). b. Find and interpret f '(12)