5. Answer all parts of this question. Each part is an independent question. i) A movie theatre treats regular customers as one market and retirees and students as another market. The demand function of regular customers is given by qi= 20 - pi and that of the retirees and students is q2 = 16 - p2. The costs of the movie theatre are given by C(q) = 6 + q* for all customers (q is the total number of customers: i.e. q = 91 +92). a) By setting up an unconstrained profit maximization problem, find the prices for the two markets and therefore the discount the retirees and students get. What is the maximum profit? Be sure to check your second-order condition. b) Does it pay for this movie theatre to price discriminate? (Hint: Compare the maximum profit above with the profit the movie theatre would be making without price discrimination.) Again, check your second-order condition. ii) Is the function 2.x f(x, y) = ya homogeneous? If so, to what degree? If it is homogeneous, prove that Euler's Theorem holds here. iii) What is the required rate of interest for a sum of money to become 3.8 times as large in 10 years, assuming continuous compounding takes place? Show your work carefully with all the steps explained in order to receive full credit. iv) An advertising company conducts a special campaign to promote sales of a certain product. They estimate that the benefits of the campaign will result in extra sales and, when the campaign is over, the extra sales, occurring in a continuous manner, will obey a curve of the form S(t) = 4000 e - 0.31 where S is the amount of extra sales and t is the time in days after the campaign is over. How many extra sales are obtained 10 days after the close of the advertising campaign