$7\mathrm{.}56)$ A $\backslash (2000\backslash$mathrm$\{$ft$\}^\{2\}\backslash )$ home in Regina is estimated to have an annual air$-$conditioning load of $\backslash (40,000\backslash$mathrm$\{$kWh$\}\backslash ).$ This home is characterized as having "medium insulation". Two air conditioners are being considered. Air conditioner $"\backslash ($ A $\backslash )"$ has a seasonal average COP of $2\mathrm{.}3$ and costs $\backslash (\backslash$$ $5500\backslash )$ to purchase and install. Air conditioner $"\backslash ($ B $\backslash )"$ has a seasonal average COP of $3\mathrm{.}6$ and costs $\backslash (\backslash$$ $7000\backslash )$ to purchase and install.

a$)$ Determine which air conditioner is the better purchase, based on the provided costing alone. Justify via simply payback period.

b$)$ State the likely installed capacity $[$tons$]$ of this air$-$conditioner, if it is expected to fully handle the home's cooling load when the summer exterior temperature reaches $\backslash (35^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Use the chart on page $4$ to support your assessment.

c$)$ Determine the maximum cost difference between option A and option B$,$ so that simple payback is no more than $10$ years $($assuming the "best option" from a$)$ above is still valid$).$