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 200 light fittings and 3100 sq ft of uninsulated exterior wall. To impress your friends, you would like to spend as much as possible, but save no more than $850 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.)

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 200 light fittings and 3100 sq ft of uninsulated exterior wall. To impress your friends, you would like to spend as much as possible, but save no more than $850 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.)

compact fluorescent light bulbs 1
insulation 2 ft2
total cost $ 3
energy costs savings $ 4 per year

Answer 1

wish I knew

Answer 2

To determine the number of compact fluorescent light bulbs and square feet of insulation to purchase, let's analyze the cost and savings data.

First, let's calculate the cost and savings for each component:

1. Compact fluorescent light bulbs:
- Cost per bulb: $4
- Energy cost savings per bulb per year: $2

2. Insulation:
- Cost per square foot: $1
- Energy cost savings per square foot per year: $0.20

Now, let's calculate the maximum number of compact fluorescent light bulbs and square feet of insulation you can purchase within the given constraints:

1. Compact fluorescent light bulbs:
- Total cost of light bulbs = Number of bulbs * Cost per bulb
- We want to spend as much as possible, so we maximize the number of bulbs while staying within the budget:
Number of bulbs = Maximum budget / Cost per bulb
= $850 / $4
= 212.5 (rounding down to 212 bulbs)

2. Insulation:
- Total cost of insulation = Area of uninsulated wall * Cost per square foot
- We want to spend as much as possible, so we maximize the area of insulation while staying within the budget:
Area of insulation = Maximum budget / Cost per square foot
= $850 / $1
= 850 square feet

Now that we have determined the maximum number of bulbs and square feet of insulation, let's calculate the energy cost savings per year:

1. Compact fluorescent light bulbs:
- Energy cost savings per year from light bulbs = Number of bulbs * Energy cost savings per bulb per year
= 212 bulbs * $2/bulb/year
= $424 per year

2. Insulation:
- Energy cost savings per year from insulation = Area of insulation * Energy cost savings per square foot per year
= 850 sq ft * $0.20/sq ft/year
= $170 per year

Finally, let's calculate the total energy cost savings per year:
- Total energy cost savings per year = Energy cost savings from light bulbs + Energy cost savings from insulation
= $424 per year + $170 per year
= $594 per year

Therefore, if you purchase 212 compact fluorescent light bulbs and insulate 850 square feet of your exterior wall, you will save approximately $594 per year in energy costs.