Question

A large part of the answer has to do with trucks and the people who drive them. Trucks come in all different sizes depending on what they need to carry. Some larger trucks are known as 18-wheelers, semis, or tractor trailers. These trucks are generally about 53 feet long and a little more than 13 feet tall. They can carry up to 80,000 pounds, which is about as much as 25 average-sized cars. They can carry all sorts of items overlong distances. Some trucks have refrigerators or freezers to keep food cold. Other trucks are smaller. Box trucks and vans, for example, hold fewer items. They are often used to carry items over shorter distances.

A lot of planning goes into package delivery services. Suppose you are asked to analyze the transport of boxed packages in a new truck. Each of these new trucks measures12 feet × 6 feet × 8 feet. Boxes are cubed-shaped with sides of either1 foot, 2 feet, or 3 feet. You are paid $5 to transport a 1-foot box, $25 to transport a 2-foot box, and $100 to transport a 3-foot box.
How many boxes fill a truck when only one type of box is used?
What combination of box types will result in the highest payment for one truckload?

Answer 1

Dimensions of the truck:

• 12 ft × 6 ft × 8 ft

Number of smallest boxes to fill the truck:

• 12×6×8 = 576 boxes

Transportation cost of smallest boxes:

• 576×5 = 2880

Number of medium sized boxes to fill the truck:

• (12/2)×(6/2)×(8/2) = 72 boxes

Transportation cost of medium boxes:

• 72×25 = 1800

Number of large sized boxes to fill the truck:

• (12/3)×(6/3)×(8/3) = 4×2×2 (whole part of the quotient) = 16 boxes

Transportation cost of large boxes:

• 16×100 = 1600

As we see the small size boxes cause the highest payment of $2880.