A carpet manufacturer in Georgia plans to expand its plant for a capital investment of $$500,000.$ The extra capacity will permit the company to produce $400,000$ yards of carpet each year during the plant$$s five$-$year life. Each yard of carpet will produce a revenue of $$2\mathrm{.}00,$ and the plant$$s incremental operating expenses are expected to be $$150,000$ each year. Assume the expansion has no salvage value at the end of year five. If the manufacturer$$s MARR is $18\%$ per year, what is the minimum annual production rate to make the expansion a worthwhile investment?

$($a$)103,400$ yards $($b$)310,000$ yards $($c$)154,950$ yards $($d$)250,350$ yards