Q$1)$ Johnson Electronics sells electrical and electronic components through catalogs printed annually. Each printing run incurs a fixed cost of $$5,000,$ which involves catalog design cost and printing setup cost. The variable production cost is $$5$ per catalog. Annual demand for catalogs is estimated to be uniformly distributed between $12,000$ and $20,000.$ Data indicate that, on average, each customer pays $$35$ for a catalog.

a$)$ How many catalogs should be printed in each run?

$[$Round up your answer to nearest integer value, e$.$g$.,2\mathrm{.}2$ and $2\mathrm{.}6$ both should be rounded up to $3.][$Enter the numerical value without commas $]$