Use lagrange multipliers to find three positive numbers whose sum is 120 and whose product is maximum. (enter your answers as a comma-separated list.) (40,40,40) incorrect: your answer is incorrect.

Using Lagrange multipliers, it is found that the numbers are: x = y = z = 40.

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The product is that we want to maximize is:

The constraint is:

The gradients are:

Their relation is:

Then, the system is:

And thus, x = y = z.

Thus:

Thus, the values are x = y = z = 40.

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