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.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.