$2\mathrm{.}2.$Suppose Pick n Pay sells $2500000$ units annually of a popular product within its Namibian operations. The cost to place, process, and receive an order from the supplier is R$100$ per order, and the cost to carry each unit of the product in the distribution center is R$0\mathrm{.}20$ per year. The acquisition cost of the product from the supplier is R$50$ per unit. Assume these costs remain constant throughout the year.

$2\mathrm{.}2\mathrm{.}1.$Calculate the economic order quantity $($EOQ$)$ for the product.

$2\mathrm{.}2\mathrm{.}2.$Based on the EOQ model, calculate the total annual ordering cost and the total annual carrying cost for the product.

$2\mathrm{.}2\mathrm{.}3.$A prospective supplier has proposed supplying $625000$ units of the product at the beginning of each quarter at a $2\%$ cash discount. Accepting this proposal would increase the annual carrying cost per unit to R$4\mathrm{.}50$ due to the need to expand the distribution center$$s capacity. The cost to place, process, and receive an order will remain R$100$ per order. Should Pick n Pay Namibia accept this proposal? Justify your decision by showing all relevant calculations.