Lagrange and math

Question 1

Explain the Lagrange multiplier method

Answer 1

Basically, we have some utility function that we wish to maximize. However, we have constraints that fuck it up for us. In order to include the constraints, we use the method of Lagrange multipliers.

The method is actually just the following:
L = f(x,y) - lambda * (constraint)

IMPORTANT: The constraint expression must be equal to 0.

Then we differentiate L(x,y,lambda) partially so that we get 3 equations that are equal to 0 (0 because maximization).

Then we use the three equations to solve for the 3 unknowns.

That’s it.

ADDITIONAL:
THe procodeydre of finding the formula is hairy as fuck. Dont bother with it.