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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?

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?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.4: Linear Programming
Problem 21E
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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?
Transcribed Image Text: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?
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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 4x+y≤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=2x+0.2y. 

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

The equations are x≤60 and y≤1100. 

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