You are thinking of making your home more energy efficient by replacingsome of the light bulbs with compact fluorescent bulbs and insulating part orall 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 footof wall insulation costs $1 and saves you an average of $0.20 per year inenergy costs.† Your home has 50 light fittings and 1,200 square feet ofuninsulated exterior wall. You can spend no more than $1,300 and would liketo save as much per year in energy costs as possible. How many compactfluorescent light bulbs and how many square feet of insulation should youpurchase? (If an answer does not exist, enter DNE.)compact fluorescent light bulbsbulbsinsulationsq ftHow much will you save in energy costs per year?

Name: You are thinking of making your home more energy efficient by replaci
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Description: You are thinking of making your home more energy efficient by replacingsome of the light bulbs with compact fluorescent bulbs and insulating part orall of your exterior walls. Each compact fluorescent light bulb costs $4 andsaves you an average of $

Answered: You are thinking of making your home…

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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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 50 light fittings and 1,200 square feet of
uninsulated exterior wall. You can spend no more than $1,300 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? (If an answer does not exist, enter DNE.)
compact fluorescent light bulbs
bulbs
insulation
sq ft
How much will you save in energy costs per year?

Expert Solution

Step 1

Consider the number of compact fluorescent bulbs to be x.

Consider the number of square feet of insulation wall to be y.

From the provided data, the constraints are,

$4 x + y \leq 1300 x \leq 50 y \leq 1200$

We also have that, $x \geq 0, y \geq 0$ because fluorescent bulbs and insulation wall quantity cannot be negative.

Maximize energy cost $p = 2 x + 0.2 y$ in accordance with the constraint given in the problem.

$4 x + y \leq 1300 x \leq 50 y \leq 1200 x \geq 0, y \geq 0$

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