Answer
$E_{save}=2.888*10^9\frac{Btu}{years}$
$Cost_{save}=12560.625\frac{dollars}{year}$
Work Step by Step
The heat output is:
$Q_{out}=5.5*10^6\frac{Btu}{h}*0.7=3.85*10^6\frac{Btu}{h}$
After tuning up the boiler the new heat input is:
$Q_{in}=\frac{3.85*10^6\frac{Btu}{h}}{0.8}=4.8125*10^6\frac{Btu}{h}$
So the heat save is:
$Q_{save}=5.5*10^6\frac{Btu}{h}-4.8125*10^6\frac{Btu}{h}=6.875*10^5\frac{Btu}{h}$
The anual energy save is:
$E_{save}=6.875*10^5\frac{Btu}{h}*4200\frac{h}{years}=2.888*10^9\frac{Btu}{years}$
And the cost save is:
$Cost_{save}=2.888*10^9\frac{Btu}{years}*\frac{4.35dollars}{10^6Btu}=12560.625\frac{dollars}{year}$
