Energy Efficiency You are thinking of making your mansion more energy efficient by replacing some of the light bulbs with LED bulbs, and insulating part or all of your exterior walls. Each LED light bulb costs $$4$ and saves you an average of $$2$ per year in energy costs, and each square foot of wall insulation costs $$1$ and saves you an average of $$0\mathrm{.}20$ per year in energy costs.$$ Your mansion has $250$ light fittings and $2,900$ square feet of uninsulated exterior wall. To impress your friends, you would like to spend as much as possible, but save no more than $$700$ per year in energy costs $($you are proud of your large utility bills$).$ How many LED light bulbs and how many square feet of insulation should you purchase? How much will you save in energy costs $($in dollars$)$ per year? $($If an answer does not exist, enter DNE.$)$ LED light bulbs : $\_\_\_\_\_\_\_\_\_\_$

insulation : $\_\_\_\_\_\_\_\_\_\_$ ft$^2$

total cost $ :$\_\_\_\_\_\_\_\_\_\_$

energy costs savings $: $\_\_\_\_\_\_\_\_\_\_$ per year