The figure provides steady$-$state operating data for an air compressor$-$intercooler system. The numbers given in MW for each of the six streams represent the exergy flow rates. Based on the recommendation of a cost engineer, it is assumed that the exergy$-$based unit costs of the compressed air $($stream $3)$ and the cooled compressed air $($stream $4)$ are equal, and there are no costs associated with the incoming air $($stream $1)$ and the supply water $($stream $5).$ The cost rates associated with the purchase and operation of the air compressor and intercooler are $$36/$h and $$72/$h$,$ respectively. Determine:

$($a$)$ The exergy destruction rates for the air compressor and intercooler, in MW$.$

$($b$)$ The exergy efficiency for the air compressor, the intercooler, and the overall system comprising these two components.

$($c$)$ The exergy$-$based unit costs of streams $3,4,$ and $6$ in cents$/$kWh$.$

$($d$)$ The cost rates associated with streams $2,3,4,$ and $6$ in $$/$h$.$

Recalculate parts $($c$)$ and $($d$)$ under the following assumption: Based on the cost engineer's recommendation, assume c$4=$c$6$c$\_4=$ c$\_6$c$4=$c$6,$ meaning the exergy$-$based unit cost of the cooled compressed air is the same as the exergy$-$based unit cost of the heated supply water. Heated Water