Minimise functions constraints help!!!?

Question

What on earth am i spoz to do for this qn?
Minimise the function;
f(x,y)=x^2+3y^2+10
subject to the constraint 8-x-y=0

Answer 1

Use lagrange multipliers. . .

If 8-x-y=0, then there's no reason we can't add it to f(x,y). And if it's truly zero, then multiplying it by lambda (L) would have no effect either.

f(x,y)=x^2+3y^2+ 10 -L(8-x-y) Now,

delf/delx=0=2x + L

delf/dely=0=6y + L And

8-x-y= 0

We have taken the equation in two unknowns and introduced the constraint by virtue of a third unknown, L. But, we have three equations, so solving is cake.

x=6

y=2

This is the minimum (58) on the y=8-x contour of the function.

Answer 2

You can us e lagrangian mult. but in this case it is so easy to put
y=8-x and y^2= 64-16x+x^2 so
f(x)=4x^2-48x+202
f´(x)=8x-48 =0 and x=6
The sign of f´(x) is ---------(6)+++++++
local minimum f(6)=58