ohnson 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. $($the same as for the previous question$)$

b$)$ Suppose that each unsold catalog can be sold to a recycling company for a price of $$1.$ What is the optimal ordering quantity?