Mark is an investor with $12,000 in capital. He is considering investing in two different stocks: Company X and Company Y. Both companies submitted a bid for a government contract and Mark believes that both companies have an equal chance of winning. Mark can buy Company X stock for $6 per share. If Company X wins the contract, each share will be worth $10, otherwise it will be worth $0. Mark can buy Company Y stock for $4 per share. If Company Y wins the contract, each share will be worth $10, otherwise it will be worth $0. Mark's utility function is = () , where is his consumption. 

a. How many shares of X and Y will he buy?