5. In 2016, UCSD completed a light-retrofitting project by replacing 20,000 40-Watt light bulbs that are
always on as they burn out with 25-Watt LED light bulbs that provide the same amount of illumination. If
the price of each regular light bulbs is $5 and the new LED light bulbs is $10 and both types of light bulbs
last one year, what is the lowest price per kWh that would justify switching to the LED light bulbs from a
pure financial perspective?
If we turn on a 40-Watt light bulb for an hour, we use 40 watt-hours of electricity. If we turn on a 25-Watt
light bulb for an hour, we use 25 watt-hours of electricity.
Assume that the electricity price is P $/kWh, then
the total cost of using 40-Watt light bulbs
=cost of purchasing the regular light bulbs + cost of electricity
the total cost of using 25-Watt light bulbs
=cost of purchasing the LED light bulbs + cost of electricity
Set the total cost of using 40-Watt light bulbs= the total cost of using 25-Watt light bulbs, and solve for P.