Burger Prince Restaurant Is Considering the Purchase of a $100,000

Burger Prince Restaurant is considering the purchase of a $100,000 fire insurance policy.The fire statistics indicate that in a given year the probability of property damage in a fire is as follows: $$\begin{array} { l c c c c c c } \text { Fire Damage } & \$ 100,000 & \$ 75,000 & \$ 50,000 & \$ 25,000 & \$ 10,000 & \$ 0 \\\hline \text { Probability } & .006 & .002 & .004 & .003 & .005 & .980\end{array}$$
a.If Burger Prince was risk neutral, how much would they be willing to pay for fire insurance?
b.If Burger Prince has the utility values given below, approximately how much would they be willing to pay for fire insurance? $$\begin{array} { l c c c c c c c } \text { Loss } & \$ 100,000 & \$ 75,000 & \$ 50,000 & \$ 25,000 & \$ 10,000 & \$ 5,000 & \$ 0 \\\hline \text { Utility } & 0 & 30 & 60 & 85 & 95 & 99 & 100\end{array}$$