Question

A package delivery service has a truck that can hold 4200 pounds of cargo and has a capacity

of 480 cubic feet.
The service handles two types of packages: small, which weight up to 25 pounds each and are no more than 3 cubic feet each; and large, which are 25 to 50 pounds
each and are 3 to 5 cubic feet each.
The delivery service charges $5 for each small package
and $8 for each large package.

Find the number of each type of package that should be
placed on a truck to maximize revenue.

x = # of small packages
Y= # of large packages

Objective Function: 5x+8y= P(x,y)

Find the constraints and explain

Answer 1

$680

Explanation:

The capacity of the truck: 4200 pounds and 480 cubic feet of cargo.

Small package: 25 pounds and 3 cubic feet each.

Large package: 50 pounds and 5 cubic feet each.

For x number of small packages:

25x pounds and 3x cubic feet

Let x = 8,

200 pounds and 24 cubic feet.

For y number of large packages:

50y pounds and 5y cubic feet

Let y = 80,

4000 pounds and 400 cubic feet.

Since delivery service charges $5 for each small package and $8 for each large package.

The maximum revenue per truck = ($5x + $8y)

= ( $5 x 8) + ($8 x 80)

= $680