1. The firm's profit function is defined by T(q, x; 3) = s(q-x) + fx-c(q). (1) The firm produces q units of output at cost c(q) such that c(0) 0, c'(q) > 0 and c"(q) > 0. The firm sells x units in the futures market at price f and sells the remaining q- x units in the spot market at random price . Assume that s takes on two values, p+ and p + E2 such that > 0> 2> -p. In other words, the random spot price is defined by the gamble (2) = where a (0, 1). (a) Write down the profit gamble conditional on q and x. (b) Set up the maximization problem of an agent with utility function u(7) such that u' (T) > 0 and u" ()