You are thinking of making your mansion more energy efficient by replacing some

Question

You are thinking of making your mansion more energy efficient by replacing some of the light bulbs with compact fluorescent bulbs, and insulating part or all of your exterior walls. Each compact fluorescent 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 $0.20 per year in energy costs.† Your mansion has 300 light fittings and 2800 sq ft of uninsulated exterior wall. To impress your friends, you would like to spend as much as possible, but save no more than $800 per year in energy costs (you are proud of your large utility bills). How many compact fluorescent light bulbs and how many square feet of insulation should you purchase? How much will you save in energy costs per year? (If an answer does not exist, enter DNE.)

Explanation / Answer

let x be the number of fluorescent bulbs to be purchased and y be the sq. fts of exterior wall to be insulated to maximize the cost.

total light bulbs = 300

uninsulated exterior wall = 2800 sq. ft

cost of 1 CFL = $4 energy saving / bulb = $2

cost of insulating wall = $1 /sq ft energy saving = $0.2 per sq. ft

Since $800 is the maximum saving so we have 2x + 0.2y = 800(

also the condition is given that spend amount should be maximum. so if all 300 required CFL bulbs are purchased (took the maximum possible number of bulbs as their cost is more than per sq ft of insulation of exterior wall). so it amounts to $600 of energy saving per year contributed by light bulbs. to make total energy saving $800 or less rest of $200 can be contributed by insulating exterior walls.

so 0.2y= 200 which implies y = 1000

300 bulbs and 1000 sq ft of exterior wall need to be insulated.

Thus the total energy saving per year would be

4*300 + 1*1000 = 2200

Thus total energy saving per year becomes 2200$

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