Chapter 14.8, Problem 24E

(a)

To determine

To find: The extreme value of the function $f\left(x,y\right)=2x+3y$ subject to the constraint $\sqrt{x}+\sqrt{y}=5$ by using Lagrange multipliers.

(b)

To determine

To compare: The values of $f\left(25,0\right)$, the value of $f\left(9,4\right)$ from part (a) and find which is greater.

(c)

To determine

To sketch: The constraint equation $\sqrt{x}+\sqrt{y}=5$ and the several level curves of the function f.

(d)

To determine

To explain: The failure of Lagrange multipliers for the given problem.

(e)

To determine

To find: The significance of $f\left(9,4\right)$.