offered an insurance contract that costs $c$ today, and will pay for any future repairs in the event it does start leaking.

$($a$)$ What is my utility if I do not purchase the insurance and my roof does not leak?

utiles.

$($b$)$ What is my utility if I do not purchase the insurance and my roof does leak?

utiles.

$($c$)$ What is my utility if I purchase the insurance?

utiles.

$($d$)$ Should I purchase the insurance if $c=36\mathrm{.}44?$

$($e$)$ What is the maximum price that I should be willing to pay for the insurance? Please round your answer to the nearest cent.

Maximum Price $=$$