Question

An office building in your community has fifty offices, each with an average of four desks. Each desk has a desk lamp that can use either a 60 watt incandescent bulb or a 13 watt fluorescent unit. The average use of a lamp is seven hours per day. How much power is required for the building per year for each of the two options? Given your local energy cost, what is the annual cost of each of the two options? If the price of an incandescent bulb is 88 cents and that of a fluorescent unit is 12 dollars, how long will it take to justify the purchase of fluorescent units, assuming everything is newly purchased?

Answer 1

Answer: Number of offices = 50; Number of desk per office =4; Bulb= 60 watts; Fluorescent = 13 watts;Average use of lamp= 7hrs

power consumed in 1 day (bulb) = 50x4x60x7= 84000 watt hrs.

power consumed in 1 day(fluoroscent unit) = 50x4x13x7=18200 watt hrs

power consumed in a year(bulb) = 84000 x 365 = 30660 KW hrs (assuming office remains open for 365 days)

power consumed in a year(fluroscent unit) = 18200 x 365 = 6643 KW hrs (assuming office remains open for 365 days)

Let say electricity cost is 15 cents/kwh.

So Annual cost by using bulb= 30660 x 15 = 4599 dollars.

Annual cost by using fluoroscent unit = 6643 x 15 = 996.45 dollars.

Given price of bulb = 88 cents; Price of fluroscent unit= 12 $

Number of lamps= 200

If bulbs are purchased, cost incurred = 200x88= 176 dollars

If fluroscent units are purchased, cost incurred = 200x12=2400 dollars

Time to justify purchase of fluroscent bulbs= ?

powe consumed by bulb per day =84 kw hr, Power consumed by fluroscent unit = 18.2 kw hrs

Let after t days fluroscent unit cost can be justified,which means equating both cost after which total cost incurred with fluoroscent unit will be less than that by bulb as yearly cost is already less

Total cost incurred after t days with bulbs (let electricity cost= 1cent/kw hr) = 84 x t x 1 + 176(price of bulbs)

Total cost incurred after t days with fluroscent unit(let electricity cost= 1cent/kw hr) = 18.2 x t x1 + 2400(price of fluroscent units)

84t + 176 = 18.2t + 2400 => t= 33.78 days i.e after 34 days cost of fluroscent unit can be justified.