Suppose D is the annual demand, H is the holding cost per unit per year, S is the ordering cost per order$).$ Then,

Find the expression for minimum total inventory cost. $($NOTE: Your expression should contain D$,$ S$,$ and H only and no other variables$).[12$ points$]$

Derive the expression for EOQ and prove that the minimum holding cost and minimum ordering cost are equal. HINT: Derivative of kx$^$n is knx$^($n$-1).$