For the cost and price functions$$ below, find $($a$)$ the$$ number, q$,$ of units that produces maximum$$ profit; $($b$)$ the$$ price, p$,$ in dollars per unit that produces maximum$$ profit; and $($c$)$ the maximum$$ profit, P$,$ in dollars.

Upper C left parenthesis q right parenthesis equals $30$ plus $5$ q e Superscript negative $0\mathrm{.}05$ q$$; p equals $15$ e Superscript negative $0\mathrm{.}05$ q

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Part $1$

Find the profit$$ function, P$.$

$$P$($q$)$equals

$$

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