Find three positive numbers whose sum is 100 and whose product is a maximum.

The numbers are;

x = 100/3,  y = 100/3,  z = 100/3

Step-by-step explanation:

Given the data in the question;

so let the numbers be; x , y and z

so

x + y + z = 100

now

G(x,y,z) = x + y + z - 100

F(x,y,z) = xyz

Fx = yz, Gx = 1

Fy = xz, Gy = 1

Fz = xy, Gz = 1

Fx = λ × Gx

yz = λ

Similarly, xz = lambda

And xy = lambda

From above clearly, x = y = z

x + y + z = 100

so

3x = 100

x = 100/3

since, x = y = z therefore, each number is equal to 100/3

x = 100/3,  y = 100/3,  z = 100/3

  the correct choice is marked

step-by-step explanation:

the first two graphs show multiple turning points. the last graphs matches the description in every detail.