Aplane delivers two types of cargo between two destinations. each crate of cargo i is 2 cubic feet in volume and 73 pounds in weight, and earns $15 in revenue. each crate of cargo ii is 2 cubic feet in volume and 146 pounds in weight, and earns $45 in revenue. the plane has available at most 130 cubic feet and 5,548 pounds for the crates. finally, at least twice the number of crates of i as ii must be shipped. find the number of crates of each cargo to ship in order to maximize revenue. find the maximum revenue.

Step-by-step explanation:

First of all, we note that Cargo II crates earn more revenue per cubit foot and more revenue per pound than Cargo I crates, so we want to maximize the shipment of Cargo II.

Since 2 crates of Cargo I must be delivered for each crate of Cargo II, it is convenient to bundle them together. Such a bundle will weigh ...

  2×73 + 146 = 292 . . . . pounds

and will have a volume of ...

  2×2 + 1×2 = 6 . . . . ft³

Then the number of bundles allowed by the volume limit is ...

  (130 ft³)/(6 ft³) = 21  2/3

and the number of bundles allowed by the weight limit is ...

  (5548 pounds)/(292 pounds) = 19

The weight limit is more restrictive, and the number of bundles it allows is an integer, so the load limit will be filled with 19 Cargo II and 38 Cargo I crates. Even though there is extra volume available, the weight limit will not allow any more cargo.

The revenue for each bundle is ...

  2×$15 +1×$45 = $75

so the maximum revenue is 19×$75 = $1425.

70,000 + 6,000 + 800 + 30

step-by-step explanation: