Answer
Energy consumption:
Electric: $24kW$
Natural Gas: $46.11kW$
Costs:
$Cost_{electric}=0.137\frac{dollars}{kWh}$
$Cost_{gas}=0.108\frac{dollars}{kWh}$
Work Step by Step
The electrical consumption is:
$W_{e}=24kW$
The heat that produces is:
$Q_{out}=24kW*0.73=17.72kW$
To produces the same heat with natural gas you will have a consumption of:
$Q_{in,gas}=\frac{17.72kW}{0.38}=46.11kW$
To obtain the unit cost of energy we just need to divide the cost of energy input by the efficiency:
$Cost_{electric}=\frac{0.10\frac{dollars}{kWh}}{0.73}=0.137\frac{dollars}{kWh}$
$Cost_{gas}=\frac{1.20\frac{dollars}{therm}*(\frac{1therm}{105500kJ})*(\frac{3600kJ}{1kWh})}{0.38}=0.108\frac{dollars}{kWh}$
