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Finding the Cost for Operating Coffee Machines

  1. May 30, 2017 #1
    1. The problem statement, all variables and given/known data
    Find the total cost for a business that operates the following for one year:

    - Fifteen 100 W light bulbs for an average of eight hours a day
    - Two 15 Ohm coffee makers connected to a 120 V power supply for two hours a day each

    The rate is 6.4 ¢/kWh

    2. Relevant equations

    ## \Delta E = P \Delta T ##

    cost = ## \Delta E ## x rate

    P = ## V^2 / R ##


    3. The attempt at a solution

    The light bulbs I thought were straight forward:

    P = 15 bulbs x 100 W = 1500 W = 1.5 kW

    ## \Delta t ## = 365 days x 8 hrs = 2920 hrs

    ## \Delta E = P \Delta t ## = (1.5 kW) (2920 hrs) = 4380 kWh

    Cost = ## \Delta E ## x rate = 4380 kWh x 6.4 ¢/kWh = 28 032 ¢ or $280.32

    The coffee makers...I figured the price of one and then doubled it.

    For one device:

    ## P = V^2 / R ##
    = ## (120)^2 / 15 Ω ##
    = 960 W = 0.96 kW

    ## \Delta T ## = 365 x 2 hrs = 730 hrs

    ## \Delta E = P \Delta T ## = (0.96 kW) (730 hrs) = 700.8 kWh

    cost = ## \Delta E ## x rate = (700.8 kWh) (6.4 ¢/kWh) = 4485.12 ¢ = $44.85

    There's two machines so x 2 = $ 89.70

    Total cost to the business for the bulbs and the coffee makers $280.32 + $89.70 = $370.02

    I am correct on the coffee machine strategy and thus the final result?
     
  2. jcsd
  3. May 30, 2017 #2
    Looks good to me. Nice work.
     
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