Problem $3(20$ points$)$

Your company has been using the economic ordering quantity to determine the lot size for one of its products it purchases from a supplier located in Sharjah. This product has an inventory holding cost of AED $2$ per unit per year and an ordering cost AED $50$ per order. The product is sold at an annual rate of $200$ units. Your company has recently implemented an ERP system, which helped to reduce the ordering cost for this product to AED $40\mathrm{.}5$ per order.

a$-$ What are the EOQ and minimum total annual cost without the ERP system $(6$ points$)$

b$-$ What are the EOQ and minimum total annual cost with the ERP system $(6$ points$)$

c$-$ If you company can only order in multiple of $200$ units, would you company benefit from the implementation of the ERP system $(8$ points$)$