Question

Three numbers x, y, and z that sum to 99 and also have their squares sum to 99. By Lagrange method, find x, y, and z so that their product is a minimum.

Answer #1

Find three positive numbers whose sum is 12, and whose sum of
squares is as small as possible, (a) using Lagrange multipliers
b)using critical numbers and the second derivative test.

Find three numbers whose sum is
3333
and whose sum of squares is a minimum.

Find the largest product the positive numbers x, y, and z can
have if x+y2+z=9. The product is (?)

Find two + numbers x and y whose product xy is 8 and whose sum
is 2x+y is a minimum

The product of two numbers is 1 and the sum of their squares is
2. Find the numbers.

(Lagrange Multipliers with Three Variables) Find the global
minimum value of f(x,y,z)=(x^2/4)+y^2 +(z^2/9) subject to x - y + z
= 8. Now sketch level surfaces f(x,y,z) = k for k = 0; 1; 4 and the
plane x-y +z = 8 on the same set of axes to help you explain why
the point you found corresponds to a minimum value and why there
will be no maximum value.

Let x, y, z be three irrational numbers. Show that there are two
of them whose sum is again irrational.

Find the minimum sum of 9x + 5y + 3z + 8 if x, y, and z are
positive numbers such that xyz = 25.

Find two positive numbers x and y whose sum is 7 so that
x^(2)*y−8x is a maximum.

Use the method of Lagrange multipliers to find the minimum value
of the function
f(x,y,z)=x2+y2+z2
subject to the constraints x+y=10 and 2y−z=3.

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