Suppose that 20 risk neutral competitors participate in a rent seeking game with a fixed prize of $500. Each player may invest as much (in $) as he wishes in the political contest. The probability of winning is directly proportional to the candidate's share of the total rent-seeking investment. a. What is the expected net benefit of a player if all other players invest $20 each? Write the net benefit as a function of the player's investment. b. Solve the maximization problem to arrive at the profit-maximizing investment. Round to the nearest cent