We are given

The endpoints are y = 0 and y = 50, each of which give A = 0 upon substitution.

To find the stationary points, we take the derivative, set it equal to zero, and solve for y:

y = 25 gives A = 100(25) - 2(25)2 = 1250, which is therefore the maximum value of A. (A has no singular points.)

Finally, the corresponding value of x is obtained by substituting y = 25 into the constraint equation x = 100 - 2y, giving x = 50.


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