Pump$-$It$-$Yourself is a new, independently owned and operated service station. As such, it will not receive regular deliveries from the local wholesale gasoline distributorship, which is controlled by a major oil company. Instead, the station will have the opportunity to purchase any or all of the excess gasoline remaining on the distributor$$s truck after all regular deliveries have been made each day. There is no delivery charge if all the gasoline remaining in the truck is taken, but if not, there is a back$-$shipping charge. The station will take all of the gasoline that it can from the truck. The delivery truck will stop each day after the station has closed for business. The amount of gasoline remaining on the truck is a random variable with the following distribution: