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sveta [45]
3 years ago
12

Find three positive numbers whose sum is 18 and whose product is maximal. (Enter your answers as a comma-separated list.)

Mathematics
1 answer:
LuckyWell [14K]3 years ago
6 0

Answer:

Step-by-step explanation:

Given that three positive numbers have sum 18.

Let the numbers be x,y, 18-x-y

Then product

f(x,y) =xy(18-x-y) = 18xy-x^2y-xy^2

To find maxima, let us use partial derivaties

f_x = 18y-2xy-y^2\\f_y =18x-x^2-2xy\\f_xx= -2x\\f_yy=-2y\\f_xy = 18-2x = f_yx

Equate I derivatives to 0

Solving the two linear equations we get solution as

(6,6)

Hence maximum when x =y=z=6

i.e. when all numbers are equal to 6.

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