# Finding the Cost for Operating Coffee Machines

1. May 30, 2017

### Catchingupquickly

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. May 30, 2017

### magoo

Looks good to me. Nice work.