For a roof of $10,000$ sqf there exist $3$ alternatives that are shown in the table. Study period$=40$ yrs and discount rate$=3\%.$ Energy $($Heating fuel$)$ cost is $$3$ per gal. Replacement of roof is $$4\mathrm{.}6$ per sqf for all alternatives and insulation cost is $$6$ per sqf for alternative $1,$ $$7$ for alternative $2,$ and $$9$ for alternative $3.$  I am giving you the answer for alternative $1$ at the next slide. Do the same for alternative $2$ and $3.$

Find: $$

$($a$)$ the Initial costs, $$

$($b$)$ the operations costs, $$

$($c$)$ the replacement costs, 

$($d$)$ the residual value for roof and insulation and perform the LCAA to find the best option. Show all your calculations.