Bill, who is also a passionate angler from Kingston, spends every weekend on Loughborough Lake to fish for walleyes (his favorite fish). Bill's preferences can be best described by the utility function U W W , where W is his wealth. Suppose that Bill's wealth is $10,000. Bill's fishing boat is 35 years old, and he knows that given its age, the market value is zero (i.e., Bill's boat does not contribute to his current wealth of $10,000). Last weekend Bill tried out his new Walleye fishing lures on Loughhorough Lake_ and noticed that his outboard engine was running low on power. Bill believes that there is a 60 percent chance that the piston rings are worn out and need to be replaced. Replacing the piston rings by a mechanic would cost $1,000. However, replacing the piston rings would not affect the value of Bill's boat (which is then still zero). Bill also believes that there is a 40 percent chance that the cylinders are completely worn gutof- round, so that the entire engine would need to be rebuilt. A local certified repair shop would charge Bill $4,000 to rebuild his engine. With a rebuilt engine his boat would be worth $2,000. Bill can bring his boat to the local repair shop. A mechanic would then thoroughly check his outboard engine, and will tell Bill whether the piston rings needs to replaced, or the entire engine needs to be rebuilt. Bill also considers buying an older used outboard engine for his boat; he found one on Marketplace for $3,000. However, installing the used engine would require some modifications, so that Bill's boat (with the used engine) would then only be worth $1,500. (Bill's old outboard engine has a zero market value.) Suppose that Bill, when not bringing his boat to the local repair shop to have his engine checked, will buy the used engine for $3,000 (instead of having both the piston rings replaced and the engine rebuilt without knowing the cause of the engine trouble). a) Suppose Bill brought his boat to the local repair shop, and the mechanic identified the cause of the engine trouble. If the piston rings need to be replaced, would Bill choose to have them replaced, or buy the used engine? If the engine needs to be rebuilt, would Bill choose to have the engine rebuilt, or buy the used engine? b) Suppose the local repair shop charges the amount P to check Bill's outboard engine. Draw a decision tree where Bill can choose between bringing his boat to the repair shop (and paying P) to have his engine checked and buying the used engine (and not bringing his boat to the repair shop). For each possible outcome write down Bill's wealth. c) What is the maximum amount P that Bill is willing to pay to the repair shop to have his engine checked?