Find two positive numbers satisfying the given requirements. the sum of the first and twice the second is 160 and the product is a maximum.

Two positive numbers x, y, such that x + 2y = 160.

The values of x and y that maximize xy.

The product will be maximized when its derivative is zero. We can write the product in terms of a single variable to make solution easier.

... y = (160 -x)/2 . . . . . solve the given relation for y

... f(x) = x·y = x(160 -x)/2 . . . . . substitute the expression for y into the product

... f'(x) = 80 -x = 0 . . . . . . . . . . find the derivative of f(x) and set it to zero

... x = 80 . . . . . . . . . . . . . . . . . add 80

... y = (160 -80)/2 = 40 . . . . . . find the value of y

The first number is 80.

The second number is 40.

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step-by-step explanation:

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step-by-step explanation:

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