Question

Consider the nonlinear optimization model stated below.

Min 2x² − 18x + 2xy + y² − 16y + 53
s.t. x + 4y ≤ 7
Find the minimum solution to this problem_____ at (x, y) = ( , )

Answer 1

To find the minimum solution, we solve the system of equations formed by the gradient of the objective function and the constraint equation.

Step-by-step explanation:

To find the minimum solution to the given nonlinear optimization model, we need to solve the system of equations formed by setting the gradient of the objective function equal to zero and the constraint equation.

First, let's find the gradient of the objective function:

∇f(x, y) = (4x - 18 + 2y, 2x + 2y - 16)

Setting the gradient equal to zero:

4x - 18 + 2y = 0

2x + 2y - 16 = 0

Solving the system of equations:

x = 2

y = 5/2

So, the minimum solution to the problem is (x, y) = (2, 5/2).