Problem $3$: A heat engine $($HE$)$ with a thermal efficiency of $35\%$ rejects $550k\frac{J}{k}g$ of heat to a sink $($low temperature reservoir$)$ at temperature of $25C.$

$($a$)$ How much heat does it receive?

$($b$)$ For the heat engine in $($a$)$ above, what is the least$/$minimum heat input possible?

$($c$)$ What is the maximum percent decrease in heat input possible? Note: the question could be stated as in parts $($a$)$ and $($c$)$ only and you have to recognize that you need to do part $($b$)$ in order to answer part $($c$).$

$($d$)$ What is your conclusion?