TechMart, a retailer specializing in high$-$end wireless keyboards, wants to optimize its inventory management for one of its most popular products. The annual demand for this wireless keyboard model is $5,000$ units. Each time TechMart places an order from its supplier, it incurs an ordering cost of $$20.$ The holding cost to store each keyboard in inventory is $$2$ per unit per year. TechMart operates $240$ days per year. The retail price for each wireless keyboard is $$50,$ and the company wants to minimize its total inventory costs, while ensuring it can meet customer demand throughout the year.

a$.$ Determine the optimal number of units per order $($EOQ$)$ to minimize total inventory costs. Round your answer to the nearest whole number.

b$.$ With the optimal order quantity $($EOQ$),$ how many times per year should the retailer place an order to meet customer demand? Round your answer to the nearest whole number.

c$.$ What is the total cost, including the annual purchase cost of items, annual holding cost, and annual ordering cost with the EOQ? Use raw values of EOQ and order frequency without rounding. Round your answer for total cost to two decimal places.

d$.$ If the holding cost increases from $$2$ to $$4\mathrm{.}1$ per unit per year, what is the new EOQ $($optimal number of units per order$)?$ Round your answer to the nearest whole number.

e$.$ Does the EOQ increase or decrease when the holding cost increases?$$

Does the EOQ increase or decrease when the holding cost increases?$$Increase or Decrease

f$.$ If the holding cost remains at $$2$ per unit per year, but the ordering cost increases from $$20$ to $$36$ per order, what is the new EOQ? Round your answer to the nearest whole number.

g$.$ Does the EOQ increase or decrease when the ordering cost increases?$$

Does the EOQ increase or decrease when the ordering cost increases?$$Increase or Decrease