The Bake Shop $($TBS$)$ buys and sells cakes. To preserve freshness TBS donates cakes that have not been sold within $5$ days to charitable organizations. To avoid waste TBS usually orders fewer cakes than it can sell. Sold out signs are frequently seen in the store. Even so$,$ the cakes come in several flavors and occasionally some of the flavors do not sell out before the $5$ day shelf life expires. Cakes cost $$17$ each to purchase and are sold for $$23$ each. During the most recent month TBS had customer orders for $29$ cakes that could not be filled due to a lack of inventory. There were only $13$ cakes that had to be donated to charity during the month. Based on this information the