The same bakery also makes gourmet chocolate-chip cookies by the dozen to sell to local grocers. The bakery is contracted to supply 30 dozen cookies a day to the grocers. (The bakery is open 300 days/year.) As the cookies will keep for several weeks once they are sealed in their packaging, the bakery will steadily make the cookies in one large batch, finish the batch, and then not make any more cookies until their inventory of cookies is depleted. (The bakery, once it starts baking, can bake 60 dozen cookies a day.)
The cookies cost us $1.00/dozen to make, and are sold to the grocers for $2.00/dozen. Because the cookies are refrigerated to extend their shelf life and because of the possibility of spoilage, the annual cost to hold the cookies in inventory is 20% of the selling price to the grocers. The cost to set up each batch is minimal; it costs $0.25 per order to prep the cooking trays, mix the dough, and to clean the equipment afterwards.
(a) How many dozen cookies should you make with each batch?
(b) How long will it take to make each batch?