Replacing incandescent lights with energy$-$efficient LED lights can reduce the lighting

energy consumption to one$-$sixth of what it was before. The energy consumed by the

lamps is eventually converted to heat, and thus switching to energy$-$efficient lighting

also reduces the cooling load in summer but increases the heating load in winter.

Consider a building that is heated by a natural gas furnace with an efficiency of $80$

percent and cooled by an air conditioner with an efficiency of $350$ percent $($this

seemingly impossible efficiency will be explained later when we cover chapter $7).$ If

electricity costs $$\frac{0\mathrm{.}12}{k}Wh$ and natural gas costs $)=({10}^9(J),$ determine if

efficient lighting will increase or decrease the total energy cost of the building $($a$)$ in

summer and $($b$)$ in winter.