Bonus question $(4$ points; these are bonus points that are counted outside of the $20\%$

assignment weight towards the course grade$)$

The Economic Order Quantity $($EOQ$)$ model minimizes the following function:

Total Inventory Management Cost$(Q)=\frac{Q}{2}*H+\frac{D}{Q}*S$

$($a$)$ Use calculus to show that TIMC is minimized at $Q=\sqrt[\phantom{2}]{\frac{2SD}{H}}.$

$($b$)$ Show that the annual holding cost and ordering cost are the same when the optimal

quantity is ordered.