A plane delivers two types of cargo between two destinations. Each crate of cargo I is 7 cubic feet in volume and 97 pounds in weight, and earns $30 in revenue. Each crate of cargo II is 7 cubic feet in volume and 194 pounds in weight, and earns $45 in revenue. The plane has available at most 455 cubic feet and 8,148 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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Asked Oct 4, 2019
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A plane delivers two types of cargo between two destinations. Each crate of cargo I is 7 cubic feet in volume and 97 pounds in weight, and earns $30 in revenue. Each crate of cargo II is 7 cubic feet in volume and 194 pounds in weight, and earns $45 in revenue. The plane has available at most 455 cubic feet and 8,148 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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Expert Answer

Step 1

According to the given information:

Let x be the number of crate of cargo I

Let y be the number of crate of cargo II

According to the question the system of equations formed is:

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maximize R 30x + 45y 7x7ys 455x+ys 65...1) 97x +194y 8148= x+2y84.(2)

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Step 2

Write the first inequality in terms of x and substitute into another that is:

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x y65y<65-x equation(2):x +2(65-x)84 x 130 2x s 84 -xs-46 x2 46 so, y s 65-x y< 65-46 ys19

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Step 3

Since the highest value of x is 46 and highest value of y is 19 so, we can assume that that maximum value will maximize the revenue....

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Math

Algebra

Linear Programming