To be turned in with Test 2. Please on these sheets in a neat, organized manner.
ID: 2080037 • Letter: T
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To be turned in with Test 2. Please on these sheets in a neat, organized manner. You may use the back of the sheets or attach additional sheets if needed. Let's take a look at why LED bulbs will likely fill your house in the future. The standard for light bulbs in the house has been the incandescent bulb, which has been around for over 100 years. These bulbs started to be phased out in 2014, and by 2020 you will likely no longer be able to purchase them for home use. Compact Fluorescent Lights (CFL bulbs) were supposed to replace them, but greaterthanorequalto has just announced that they will no longer make or sell CFL's in the US by the end of 2016. Instead, the new standard appears to be Light Emitting Diodes (LED bulbs) As research on LEDs has progressed, the price of an LED bulb for home use has dropped from about $100 per bulb to about $5 per bulb. A typical LED bulb that uses 10 W has an average lifespan of about 25000 hours. This bulb produces light that is equivalent to a 60W incandescent bulb that has an average life span of 1200 hrs and costs about $1 per bulb. Let's calculate the impact of switching from 60 W incandescent bulbs to 10 W LED bulbs. Assuming your LED bulb lasts the typical 25000 hr lifespan, how many years will it be before the bulb needs to be replaced if you turn it on for 4 hours a day, every single day of the year? If you replace the 5 most used bulbs in your house (assume each bulb is on for 4 hours every day of the year) from 60 W incandescent bulbs to 10 W LED bulbs, how much money will you save over the life of the LED bulb, including the cost of the bulbs? Assume electricity costs $0.15/k Based on those life-of-the-bulb savings, how much will you save per year by switching just these 5 bulbs in your house? Granted, it will cost you more up front to put in the more expensive LED bulbs. However, based on the savings you calculated, how long will it take you recover the additional cost of the LED bulbs compared to the cost of incandescent bulbs?Explanation / Answer
Given data: 1) 60 W incandescent bulb : Lifespan = 1200 hours, cost =$1 per bulb
2) 10 W LED : Lifespan = 25000 hours, cost = $5 per bulb
a) Time of operation of LED bulb = 4 hours a day (every single day of the year)
Lifespan = 25000 hours
Years needed to replace the LED Bulb = 25000/4 = 6250 days = 17 years 45 days.
b) case 1: 60 W incandescent bulb in operation
Number of bulbs = 5 numbers
Time of operation = 4 hours a day (every single day of the year)
Time period considered for calculating savings = life span of LED bulb= 25000 hours
Electricity Cost = $0.15/kWhr
Cost of the bulb =$1 per bulb
Energy Consumed by 5 bulbs = 5* 60 * 25000 = 7500kW
Total energy cost = $0.15 * 7500 = $1125
Number of times to replace incandescent bulb in a period of 25000 hours = 25000/1200 = 20 times
Cost of bulb replacement = $1 * 5 * 20 = $100
Therefore total cost = $1125 + $100 = $1225
case 2: 10 W LED bulb in operation
Number of bulbs = 5 numbers
Time of operation = 4 hours a day (every single day of the year)
Time period considered for calculating savings = life span of LED bulb= 25000 hours
Electricity Cost = $0.15/kWhr
Cost of the bulb =$5 per bulb
Energy Consumed by 5 bulbs = 5* 10 * 25000 = 1250kW
Total energy cost = $0.15 * 1250 = $187.5
Number of times to replace LED bulb in a period of 25000 hours = 25000/25000 = 1 time
Cost of bulb replacement = $5 * 5 *1 = $25
Therefore total cost = $187.5 + $25 = $212.5
Therefore, money saved over the life span of LED bulb = $1225 - $212.5 = $1012.5
c) Time of operation considered = 1 year ( 4* 365 = 1460 hours of operation)
Savings for 25000 hours (25000/1460 = 17.12 years) = $1012.5
Savings per year = $1012.5/ 17.12 = $59.14
d) Let X be the number of days to recover the additional cost of LED bulbs compared to the cost of incandescent bulbs.
Energy cost of 5 numbers of 60W Incandescent bulb per day = ($0.15 * 5 *60 *4/1000) = $0.18
Cost of 5 numbers of 60W Incandescent bulb = $1 * 5 = $5
Total cost for X days of Incandescent bulb operation = $0.18 * X + $5
Energy cost of 5 numbers of 10W LED bulb per day = ($0.15 * 5 *10 *4/1000) = $0.03
Cost of 5 numbers of 10W LED bulb = $5 * 5 = $25
Total cost for X days of LED bulb operation = $0.03 * X + $25
For getting recovery by using LED bulbs, $0.03 * X + $25 = #0.18 * X + $5
Solving for X, we get 0.15 X = 20
X = 133.33 days.
(note : If X exceeds 300 days (1200/4), incandescent bulb should be replaced. therefore, additional $5 should be added to the total cost of incandescent bulb and again X is recalculated. Here X= 133.33 days only. therefore 133.33 days is the final answer)
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