From Paul's Online Notes (Business Applications Practice Problems) The production costs, in dollars, per week of producing x widgets is given by C(x) = 4000 - 32x + 0.08x2 + 0.00006x3 and the [inverse] demand function (price of widget based on quantity demanded by the market) for the widgets is given by p(x) = 250 + 0.02x - 0.001x2 P (x ): 202 - 0 coax (a) The marginal cost is the derivative of the production cost function, C(x), with respect to the number of widgets produced per week. Find the marginal cost as a function of the number of widgets produced per week. P(x ) = 0+ 0102x120 - 0.001 x 2x : 0 +0.02 - 0.002x = 0. 02- 0.002X (b) The revenue R(x) is the product of the demand (number of widgets demanded by the market) and the corresponding market price (at that demand level). This means the revenue function is given by: R (x ) = x . p (x ) Find R(x) explicitly. R' (x ) = 250 + 0. 04x - 0.003x2 (c) The marginal revenue is the derivative of the revenue with respect to the number of widgets produced per week. Find the marginal revenue as a function of the number of widgets produced per week