A new model of widget can be produced for $5 per widget and x widgets can be sold for p = (500.001x) (in dollars) each. a.Find, where x is the number of units sold, the revenue function, R(x) in dollars. b.Find the maximum revenue and the quantity x where revenue is maximized. c. i. Find the cost function C1(x) if there is a fixed cost of $450,000: ii. ii. Find the cost function C2(x) if there is a fixed cost of $505,000: d. i. Determine (algebraically) x, the number of units made and sold, such that R(x) = C1(x) for C1(x) found in part (C). ii.Determine (algebraically) x, the number of units made and sold, such that R(x) = C2(x) for C2(x) found in part (C). e.Sketch the revenue function and the two different cost functions in the same coordinate system.