Discount$-$Mart, a major East Coast retailer, wants to determine the economic order quantity for its halogen lamps. It currently buys all halogen lamps from Specialty Lighting Manufacturers, in Atlanta. Annual demand is $2,000$ lamps, ordering cost per order is $$0\mathrm{.}50,$ canying cost per lamp is $$20.$ As part of its new JIT program, Discount$-$Mart has signed a long$-$term contract with Specialty Lighting and will place orders electronically for its halogen lamps.

a$)$ What is the economic order quantity? $10$ units per order $($round your response to the nearest whole number$).$

b$)$ How many orders will be placed? per year $($round your response to the nearest whole number$).$