A plane delivers two types of cargo between two destinations. Each crate of cargo I is 9 cubic feet in volume and 187 pounds in weight, and earns $30 in revenue. Each crate of cargo II is 9 cubic feet in volume and 374 pounds in weight, and earns $45 in revenue. The plane has available at most 540 cubic feet and 14,212 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. crates of cargo I crates of cargo II maximum revenue $

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AlonsoDehner AlonsoDehner · Answer 1 · 2020-03-06T01:39:44+01:00

Answer:

So maximum when 46 of I grade and 16 of II grade are produced.

Max revenue = 2100

Step-by-step explanation:

Given that a plane delivers two types of cargo between two destinations

Crate I Crate II

Volume 9 9

Weight 187 374

Revenue 30 45

Let X be the no of crate I and y that of crate II

Then

[tex]9x+9y\leq 540\\187x+374y\leq 14212\\x\geq 2y[/tex]

Simplify these equations to get

[tex]x+y\leq 60\\x+2y\leq 76\\x\geq 2y[/tex]

Solving we get

[tex]y\leq 16\\x\leq 46 and x\geq 32\\32\leq x\leq 46[/tex]

REvenue = 30x+45y

The feasible region would have corner points as (60,0) or (32,16) or (46,16)

Revenue for (60,0) = 1800

(32,16) = 1680

(46,16)=2100

So maximum when 46 of I grade and 16 of II grade are produced.

Max revenue = 2100