I am quite confuse with the explaination of Shadow Price found from Internet.

It can be understood as: the value of an addition revenue if the constraint is relaxed.

or

How much you would be willing to pay for an additional resource.

The problem:

maximize 5x1 + 4x2 + 6x3
subject to 6x1 + 5x2 + 8x3 <= 16   (c1)
10x1 + 20x2 + 10x3 <= 35           (c2)
0 <= x1, x2, x3 <= 1


Solving this problem, we get the shadow price of c1 = 0.727273, c2 = 0.018182.

Comparing c1 and c2, if 1 constraint can be relaxed, we should relax c1 instead of c2?

Thanks..

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In the example you give, there are 16 units available of the first resource and 35 units available of the second resource. The fact that the shadow price of $c_1$ is 0.727273 means that if you could increase the first resource from 16 units to 17 units, you would get an additional profit of about \$0.73. Similarly, if you could increase the second resource from 35 units to 36 units then you would get an additional profit of about \$0.02.