Use a Lagrange multiplier to optimize the following function subject to the given constraint and estimate the effect on the value of the value of the objective function from a 1-unit change in the constant of the constraint (i.e. obtain solution, substitute, and evaluate the function, take note of Lagrange multiplier value).

Then, solve the same problem with the constraint modified to be:

Explain what you find. What is the meaning of the Lagrange multiplier?

\\( x+y=72 \\) s.t. \\( z=4 x^{2}-2 x y+6 y^{2} \\) \\( x+y=73 \\)