$6\mathrm{.}1$ Suppose you purchase a part from a supplier for a unit cost of $$4$ with which you assemble red widgets. On average, you use $50,000$ units of this part each year. Every time you order this particular part, you incur a sizable ordering cost of $$800$ regardless of the number of parts you order. Your cost of capital is $20\%$ per year.

a$.$ How many parts should you purchase each time you place an order?

b$.$ To satisfy annual demand, how many times per year will you place orders for this part?