Suppose your firm purchases a $$4$ per unit part from a supplier. Your firm uses the part to assemble red widgets. On average, you use $50,000$ units of this part each year. Every time you order this particular part, you incur a sizable ordering cost of $$800,$ regardless of the number of parts you order. Your cost of capital is $20\%$ per year, and your unit holding cost per year is $10\%.$ How many parts should you purchase each time you place an order $($i$.$e$.,$ what is the optimal order quantity$)?$ Round a number to the nearest whole number.

Group of answer choices

$8165$

$9200$

$5378$

$4239$