(C) Now let's maximize E [U 1(X )] as a function of B. (1) By considering the three different cases for p mentioned above, and with par- ticular reference to your sketches in (b), briey explain why Bf, the optimal B under U1, is as follows: 0 (don't bet) for p % (ii) Compute the rst partial derivative of E [U1 (X )] as a function of B, and try setting it equal to U and solving for B. With reference to your sketches in (b), briey explain why this standard calculus approach to maximizing a function won't work in this problem. (iii) Identify one feature of this betting strategyr that seems reasonable, and two features that seem unreasonable; explain briey. Someone offers you the possibility to play a gambling game with the following rules. First, you decide how much money you're willing to put at risk in this game: this amount let's call it A > 0 is referred to as your stoke (all the monetary quantities are in dollars in this problem); think of A as a xed known positive real number in what follows. Having chosen your stake, you're allowed to bet any amount 0 g: B g A (thus, as a decision problem, your possible actions in this situation correspond to values of B). If you win the bet, which occurs with probability 0