Use Lagrange multipliers to find the indicated extremum. Assume that x and y are positive.

Question

Use Lagrange multipliers to find the indicated extremum. Assume that x and y are positive.

Minimize f(x,y)= x^2-y^2

Constraint: x-10y+198=0

Find the minimum of f(x,y)= ______ at (x,y)= (_______)

Answer 1

f(x,y) = -396 @ (x,y) = (2,20)

Taking Del f = λDel C leads to 2x = λ and 2y = 10λ.

or

y = 10x putting this into the constraint, we get x - 100x + 198 = 0 or x = 2, then y = 20.

Substituting into f(x,y) you get -396