The Following Results Are Obtained When Optimizing F(x, Y)subject to the Constraint

Essay

The following results are obtained when optimizing f(x, y)subject to the constraint g(x, y)= 39.The maximum value is f(5, 7)= 42, the Lagrange multiplier $\lambda$ = 3 (when $\nabla f = \lambda \nabla g$ )and $\nabla f = 3 \vec { i } - 3 \vec { j }$ .If the constraint condition is changed to g(x, y)= 40, what will be new maximum value of f(x, y)?