An office building is considering converting from a coal$-$burning furnace to one that burns either fuel oil or natural gas. The cost of converting to fuel oil is estimated to be $$80,000$ initially; annual operating expenses are estimated to be $$4,000$ less than that experienced when using the coal furnace. Approximately $140,000$ Btus are produced per gallon of fuel oil; fuel oil is anticipated to cost $$2\mathrm{.}20$ per gallon.

The cost of converting to natural gas is estimated to be $$60,000$ initially; additionally, annual operating and maintenance expenses are estimated to be $$6,000$ less than that for the coal$-$burning furnace. Approximately $1,000$ Btus are produced per cubic foot of natural gas; it is estimated that natural gas will cost $$0\mathrm{.}04$ per cubic foot.

A planning horizon of $20$ years is to be used. Zero market values and a MARR of $10\%$ per year are appropriate. Perform a sensitivity analysis for the annual Btu requirement for the heating system.

$($Hint: First calculate the breakeven number of Btus $($in thousands$).$ Then determine AWs if the Btu requirement varies over $+-30\%$ of the breakeven amount. Use increments$/$decrements of $10\%$ in your analysis.$)$