A college textbook publisher sells a certain e$-$book for $$40\mathrm{.}50.$ For the current process, the publisher has fixed cost of $$335,000$ and a variable cost per book of $$32\mathrm{.}00.$

a$.$ What is the break$-$even quantity for this book? Round your answer to the nearest whole number.

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b$.$ If the variable cost increased by $11$ percent due to poor operating performance, what is the new break$-$even quantity? Round your answer to the nearest whole number.

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c$.$ If through better process efficiency the fixed cost decreases by eleven percent and the variable cost decreases to $$31\mathrm{.}10,$ what is the revised break$-$even quantity? Round your answer to the nearest whole number.

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