Problem Set C 1. Dugicel's profit function for the sale of 521 15 as follows: t(q) = 2q% + 3509 150 The selling price per 521 is given by the function: p = 600 2q Where g represents the number of 521 (in thousands), cost and revenue are in thousand of dollars. Using the information provided above, determine the following: a. Total Cost function. Marginal Cost (MC) when 4000 521 are produced. (G1ve an interpretation of yvour answer from Part b. above. The number of 521 that must be sold for Digicel to make a Marginal Revenue (MR) of $300,000.00. At what level of quantity will the firm maximize its profit. [4 marks] [2 marks] [1 mark] [4 marks] [4 marks] 2. Differentiate the following: a. q(p) = 3e3 - 2p : [2 marks] b. y = In (5p 2 - vp) [4 marks] c. f'(1) = (3e3 - 2p =) In (5p-2 - Vp) [4 marks] 3. Given Flow's Total Cost function: TC(x) = 2x3 - 66x* + 576x + 1000 Use the first and second derivative principles to determine the level of output (in thousand) at which the firm's cost is minimized. [8 marks]