Question

Minimize
Q= 6x² + 3y² where x+y=9

Answer 1

To minimize the function Q= 6x² + 3y² subject to the constraint x+y=9, we can use the method of Lagrange multipliers.

Step-by-step explanation:

To minimize the function Q= 6x² + 3y² subject to the constraint x+y=9, we can use the method of Lagrange multipliers. First, we express the constraint equation in the form g(x,y) = 0:

x+y-9=0

Next, we form the Lagrangian function: L(x,y,λ) = Q - λ(g(x,y))

We then take the partial derivatives of L with respect to x, y, and λ, and set them equal to zero to find the critical points. Solving the system of equations will give us the values of x, y, and λ that minimize Q.