An industrial machine tools manufacturer buys parts from a supplier. For a particular part, the monthly demand is expected to average $750$ units. Ordering is done by phone and is estimated to cost $$50,$ including the cost of a quick parts inventory and payment. The company has determined that its inventory carrying costs are $25\%$ per year. The product is valued at the suppliers facility at $$35$ each. They charge $$3$ per part to have them shipped to the manufacturer$$s facility.

$[1]$ What is the recommended economic order quantity for this product? $(17$ points$)$

$[2]$ How many times a year will you reorder the product? $(4$ points$)$

$[3]$ Assume that the parts come in cases of $100.$ What would your order size be$?(4$ points$)$

Show all of your calculations.