Consumers' Surplus The demand function for a certain brand of mattress, is given by

$p=450e^{-0\mathrm{.}05x}$

where $p$ is the unit price in dollars and $x($in units of a hundred$)$ is the quantity demanded per month.

$($a$)$ Find the number of mattresses demanded per month if the unit price is set at $$\frac{200}{?}$ mattress. $($Round your answer to the nearest integer.$)$

mattresses

$($b$)$ Use the results of part $($a$)$ to find the consumers' surplus if the selling price is set at $$200$ per mattress. $($Round your answer to the nearest dollar.$)$

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