$5($a$)\_$#$3$: A heat pump must supply $50,000$ Btu$/$h on a $30$ oF day to maintain the temperature of a

house at $72$ oF$.$

a$)$ Determine the maximum coefficient of performance for this heat pump.

b$)$ What is the minimum power input, hp$,$ for this heat pump? $(1\mathrm{.}55$ hp$)$

c$)$ If the electricity cost is $8\mathrm{.}5$ center per kWh$,$ calculate the minimum cost to run this heat

pump for one week. $($$$16\mathrm{.}52/$month$)$

d$)$ Assuming that the power input that is available is in $1$ hp increments, determine actual

COP and the corresponding increase in cost for one week for the closest available size.

$(28\mathrm{.}9\%)$