McTavish Transportation loads Intermodal containers onto railcars. Each railcar can accommodate a maximum size load of 60 feet long x 8 feet wide x 8 feet high. McTavish only loads three sized of intermodal containers:
Container size (L x W x H) (in feet)
10 x 8 x 8
20 x 8 x 8
55 x 8 x 8
Price charged to customer:
Variable cost per container
McTavish currently has space available on 10,000 railcars. No additional railcars are available.
Fixed costs related to loading the railcars is $80,000. This is allocated at $8 per foot of length. (For example, a Short container would be allocated $80 in fixed costs)
Various customers have the following containers to be loaded. Total demand is as follows:
Short: 36,000 containers
Standard: 18,000 containers
Long: 3,000 containers
McTavish can pick and choose which containers are loaded and which customers to accept.
How many rail cars would be required to satisfy all of the current demand?
How many of each container type should McTavish load?