A manager receives a forecast for next year. Demand is projected to be $510$ units for the first half of the year and $900$ units for the second half. The monthly holding cost is $$2$ per unit, and it costs an estimated $$55$ 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$.,85$ 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. $($Round your answers to the nearest whole number.$)$

b$.$ If the vendor is willing to offer a discount of $$10$ per order for ordering in multiples 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? $($Round intermediate calculations to $2$ decimal places.$)$