Binary Choice$$sells new desktop and laptop computers. $$Their supplier for charges $$60$ per order, and holding cost is $$150$ per unit.$$ They sell $50$ computers per month. $$The manufacturer has offered the following price schedule:

Order Quantity

Price Per Unit

$<11$

$$520$

$12$ to $64$

$$500$

$65$ to $128$

$$495$

$>128$

$$485$

a$)$ What order quantity minimizes total annual inventory cost?

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b$)$ The supplier has offered to be a drop shipper, i$.$e$.,$ they will ship directly to the customer.$$ In exchange, they will increase the unit price to $$515$ per computer, but not charge the ordering costs and all inventory will be held at the supplier.$$ From a purely financial standpoint, should Zeus take them up on the offer?