PROBLEM $6(10$ points$).$ A petroleum company, whose minimum attractive rate of return is $10\%,$ needs to paint the vessels and pipes in its refinery periodically to prevent rust. "tuff$-$Coat", a durable paint can be purchased for $$8\mathrm{.}05$ per gallon while "Quick$-$Cover", a less durable paint, costs $$3\mathrm{.}25$ per gallon. The labor cost applying a gallon of paint is $$6\mathrm{.}00.$ Both paints are equally easy to apply and will cover the same area per gallon. "Quick$-$Cover" is expected to last $5$ years and "Tuff$-$Coat" is expected to last $11$ years. Which paint do you recommend?