- #1
tnutty
- 326
- 1
Homework Statement
Find mix/max
2x + 6y + 10Z bounded by x^2 + y^2 + z^2 = 35
After finding the partial derivative and letting it equal to the bounding equation * C
2 = C * 2x
6 = C * 2y
10 = C * 2z
x^2 + y^2 + z^2 = 35
x = 1/C
y = 3C
z = 5C
inputting this into the equation of sphere
(1/C)^2 + (3C)^2 + (5C)^2 = 35
=
1/C^2 + 9C^2 + 25C^2 =35
=
1/C^2 + 34C^2 = 35
now I tried a couple of different things and I think the simplest for I got it down to was
this :
1 = (35 - 34C^2) C^2
It looks like C = plus/minus 1 from observation, but that's not deductive enough, and way
to show it with math, and not just plugging it in please.
From there If I find the constant C the I can try to find other variables , x, y, z