What is the optimal profit? A plane delivers weight, and earns $35 in revenue. E

Question

What is the optimal profit? A plane delivers weight, and earns $35 in revenue. Each crate of cargo II is 3 cubic feet in volume and 224 pounds in weight, and earns $45 in revenue. The plane has available at most 270 cubic feet and 12,544 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 two types of cargo between two destinations. Each crate of cargo I is 3 cubic feet in volume and 112 pounds in maximum revenue crates of cargo I maximum revenue crates of cargo 11 maximum revenue $

Explanation / Answer

Solution:

Let x represent the number of crates of cargo 1

Let y represent the number of crates of cargo 2

Give the two inequalities that x and y must satisfy because of the plane capacity

volume

3x + 3y =<270

weight

112x +224y =< 12544

objective function Maximize p = 35x + 45 y

using simplex theorem

Maximize p = 35x + 45y subject to
3x+3y<=270
112x +224y <=12544

Tableau #1
x y s1 s2 p
3 3 1 0 0 270   
112 224 0 1 0 12500  
-35 -45 0 0 1 0   

Tableau #2
x y s1 s2 p
1.5 0 1 -0.0134 0 102
0.5 1 0 0.00446 0 56   
-12.5 0 0 0.201 1 2520   

Tableau #3
x y s1 s2 p
1 0 0.667 -0.00893 0 68
0 1 -0.333 0.00893 0 22
0 0 8.33 0.0893 1 3370  

from above tableau

Optimal Solution: p = 3370; x = 68, y = 22

therefore

crate 1 = 68

crate 2 = 22

maximum reveue = 3370

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