A manufacturing company places a semi$-$annual order of $24,000$ units at a price of $$20$ per unit. Its carrying cost is $15\%$ and the order cost is $$12$ per order. Include the formulas and show your work for each part. Refer to the rubric for detailed evaluation.

Required:

$1.$ What is the most economical order quantity?

$2.$ How many orders need to be placed?

$3.$ How often should an order be placed?