Question $1$: EOQ, quadratic holding cost $[15$ points$]$

Recall that in EOQ, we assume that the rate at which cost accrues due to holding inventory

amount I$($t$)$ at a moment in time t is h I$($t$).$

Calculate what the optimal order quantity would be if this were instead h I$($t$)^2.$ Assume, as we

do in EOQ, that the time over which we calculate cost is a multiple of T$.$

Hint: use an integral to calculate the total holding cost over one cycle. Then divide by T to get

the average holding cost per unit time.