$($EOQ problem$)$

A manager receives a forecast for next year. Demand is projected to be $750$ units for the first half of the year and $1100$ units for the second half. The monthly holding cost is $$1$ per unit, and it costs an estimated $$50$ to process an order.

$($a$)$ Assuming that monthly demand will be level during each of the six$-$month periods covered by the forecast $($e$.$g$.,100$ per month for each of the first six months$),$ determine an order size that will minimize the sum of ordering and carrying costs for each of the six$-$month periods.

$($b$)$ If the vendor is willing to offer a discount of $$5$ per order for ordering in multiple of $50$ units $($e$.$g$.,50,100,150),$ would you advise the manager to take advantage of the offer in either period? If so$,$ what order size would you recommend?