Equipment purchased $2$ years ago by Newport Corporation to make pneumatic vibration isolators cost $$105,000.$ It has a market value that can be described by the relation $$105,000$ $$8,200$k$,$ where k is the years from time of purchase. The operating cost for the first $5$ years is $$54,000$ per year, after which it increases by $$5,500$ per year. The assets salvage value was originally estimated to be $$7000$ after a predicted $10-$year useful life. Determine the values of P$,$ S$,$ and AOC if $($a$)$ a replacement study is done now and it is assumed that the equipment will be kept a maximum of one more year, and $($b$)$ a replacement study is done $5$ years from now and it is assumed that the equipment will be kept a maximum of only one more year after that.

a$)$The value of P is $ $.$

The value of S is $ $.$

The value of AOC is $ $.$

b$)$The value of P is $ $.$

The value of S is $ $.$

The value of AOC is $ $.$