$(50$ points$)$ You are trying to reduce your water consumption at home to be more environmentally friendly, as well as reduce your monthly water bill. You have a toilet that uses $3\mathrm{.}6$ gallons per flush, a showerhead that uses $2\mathrm{.}5$ gallons per minute, and a washing machine that uses $40$ gallons per load. On average, you flush the toilet $3$ times a day, take a $10-$minute shower every day after working out, and use $4$ loads of laundry per month. Your water provider charges you $$10$ per CCF $(1$ CCF $($hundred cubic feet$)=748$ gallons$).$ a$.$ Calculate your current yearly water consumption in CCF and your yearly water bill. b$.$ If you were to replace your old appliances with a new $$125$ toilet that uses $1\mathrm{.}28$ gallons per flush, a $$20$ showerhead that uses $1\mathrm{.}5$ gallons per minute, and a $$400$ washing machine that uses $27$ gallons per load. What does your yearly water consumption in CCF$,$ and water bill end up being? c$.$ How much less water do you end up consuming, and by how much does your water bill decrease? d$.$ How long does it take to get your payback, or return on investment, for each appliance when comparing to their older model? Which has the faster return?