V. [15 points] A travel agency has a cost function C (q) and a revenue function R(q) given by C(q) = 10,000 + 3412 and R(q) = 450g, both in dollars, Where q is the number of tickets sold. (a) Write an equation for the prot function 7r(q), the travel agency's prot as a function of the quantity of tickets sold, q. (b) Assuming that the company can sell any number of tickets between 0 and 100, that is, 0 S q S 100. Find the quantity, q, that maximizes the prot function