$6.$ Somerset Corporation purchases a particular brand of microchip used in the assembly of computers directly from the supplier. It costs the company RM$8$ each time it places an order with the manufacturer for the microchips. The supplier will deliver order of any size for a charge of RM$4$ and cost of holding an item in inventory for a year is estimated to be $20\%$ of the cost price. Samuel, the store manager estimates that total annual demand for the microchip will be $600$ units, with a constant demand rate throughout the year. Currently, the store is making $250$ orders, two times in a month. Goods are received $10$ days after an order has been placed. The store is open for business $300$ days in a year.

a$)$ Calculate the total inventory cost based on the current ordering policy.

b$)$ Compute the optimum order quantity and calculate the associated minimum total inventory cost.

c$)$ Based on the optimum order quantity, determine the reorder point.

d$)$ If the supplier offers large order discounts of $8\%$ and $10\%$ for single order quantities of minimum $400$ and $500$ respectively, should the company change its ordering policy?