Willy’s only source of wealth is his chocolate factory. He has the utility function , where p is the probability of a flood, and cf and cnf are his wealth contingent on a flood and on no flood, respectively. The probability of a flood is p = 1/6. The value of Willy’s factory is $500,000 if there is no flood and$0 if there is a flood. Willy can buy insurance where if he buys $x worth of insurance, he must pay the insurance company$2x/17 whether there is a flood or not, but he gets back \$x from the company if there is a flood. What is the value x of insurance that Willy should buy? If Willy buys this insurance what will his wealth be in case of a flood and no flood, respectively?