Question

is the average cust t0 2-39 LED light bulbs are more energy efficient, last longer, cost more, and have a smaller environmental impact from manufacture to recycling or disposal. The question is which costs less: incandescent, compact fluorescent (CFL), or LED lights? Incandescent CFL LED Cost/bulb Life in hours Watts usecd $0.50 1250 60 $2 $7 8333 25,000 14 (a) Ignore the time value of money. What is the average cost per hour for 25,000 hours of light- ing in a community with $0.15/kWh electricity for each choice? (b) If the light is on 5%, 30%, or 60% of the time, how long until does it take for the 25,000 hours? (c) Which type of light should a homeowner buy?

For engineering economic analysis class

Answer 1

Solution

(A) We need to calculate the average cost per hour in each case.

Total Cost = Electricity cost + Bulb cost

The electricity cost / tariff remains constant since all the bulbs are tested in the same area.

Electricity cost = $0.15 / kWh

1 kWh = 1000 watts for 1 hour

Number of Hours = 25,000 hours

Calculating the Average cost per hour

Incandescent bulbs - 60 W meaning 60 w of power used in hour i.e.,0.06 kWh

Number of bulbs needed for a period of 25,000 hours = (25000 /1250) i.e.,20 bulbs

Total cost = (0.5 * 20) + (0.06 * 0.15)

= $10.01

Average cost per hour = 10 / 25000

CFL bulbs - 14 W meaning 14 w of power used in hour i.e.,0.014 kWh

Number of bulbs needed for a period of 25,000 hours = (25000 /8333) i.e., 3 bulbs

Total cost = (2 * 3) + (0.014 * 0.15)

= $ 6.0

Average cost per hour = 6/ 25000

LED bulbs - 7 W meaning 7 w of power used in hour i.e.,0.007 kWh

Number of bulbs needed for a period of 25,000 hours = (25000 /25000) i.e., 1 bulb

Total cost = (7) + (0.007 * 0.15)

= $7.00

Average cost per hour = 7 / 25000

Therefore CFL cost the least

(C) The homeowner should buy CFL bulbs as the average cost per hour is the least.

(B) Let X be the required number of hours in order to complete 25,000 hours

Light is on for 5% => .05 * (X) = 25000  

i.e., 5,00,000 hours

Light is on for 30% =>0.3 * (X) = 25000  

i.e., 83,333.33 hours

Light is on for 5% => 0.6 * (X) = 25000  

i.e., 41,666.67 hours

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