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Southeast Pools uses cost$-$plus pricing with a $30\%$ mark$-$up on total cost. The company is currently building $320$ pools per year with total variable cost of $$5,760,000.$ In addition, the company incurs $$720,000$ in fixed costs annually and has a capacity to build $450$ pools.

$($a$)$

How much will the company price each pool on average?

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$($b$)$

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