31. ENERGY EFFICIENCY You are thinking of making your home more energy efficientby replacing some of the light bulbs with compact fluorescent bulbs and insulatingpart or all of your exterior walls. Each compact fluorescent light bulb costs $4 andsaves you an average of $2 per year in energy costs, and each square foot of wallinsulation costs $1 and saves you an average of $0.20 per year in energy costs.*Your home has 60 light fittings and 1,100 square feet of uninsulated exterior wall.You can spend no more than $1,200 and would like to save as much per year inenergy costs as possible. How many compact fluorescent light bulbs and howmany square feet of insulation should you purchase? How much will you save inenergy costs per year?

Name: 31. ENERGY EFFICIENCY You are thinking of making your home more energ
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Description: 31. ENERGY EFFICIENCY You are thinking of making your home more energy efficientby replacing some of the light bulbs with compact fluorescent bulbs and insulatingpart or all of your exterior walls. Each compact fluorescent light bulb costs $4 andsav

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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31. ENERGY EFFICIENCY You are thinking of making your home 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 home has 60 light fittings and 1,100 square feet of uninsulated exterior wall.
You can spend no more than $1,200 and would like to save as much per year in
energy costs as possible. 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?

Expert Solution

Step 1

Given:

The cost of each compact fluorescent bulb is $$ 4$ and the cost of each square foot of wall insulation is $$ 1$ . The maximum cost we can spend is $$ 1200$ .

If $x$ is the number of compact fluorescent light bulbs and $y$ is the number of square feet of insulation, the equation is given as $4 x + y \leq 1200$ .

Energy cost saved using compact fluorescent bulb is $$ 2$ and the energy cost saved with wall insulation is $$ 0.20$ . We are asked to find the maximum energy cost saved.

The equation is $P = 2 x + 0.2 y$ .

There are a total of $60$ light fittings and $1100$ square feet of uninsulated exterior wall.

The equations are $x \leq 60 and y \leq 1100$ .

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