### Problem Statement**Objective:** Maximize the function \( f(x, y) = \sqrt{18 - x^2 - y^2} \).**Subject to the constraint:** \( x + y - 2 = 0 \).### ExplanationIn this problem, we are provided with a multivariable function \( f(x, y) \), which we need to maximize. The function is given by:\[ f(x, y) = \sqrt{18 - x^2 - y^2} \]Additionally, we have a constraint equation:\[ x + y - 2 = 0 \]This means that the values of \( x \) and \( y \) must satisfy this equation.### Details- \( f(x, y) \) represents a function with two variables \( x \) and \( y \).- The term \( \sqrt{18 - x^2 - y^2} \) suggests that the function is related to a circular region as the square root function ensures that the domain is limited by the condition \( 18 - x^2 - y^2 \geq 0 \).- The constraint \( x + y - 2 = 0 \) is a linear equation representing a line in the \( xy \)-plane.To solve this problem, one might typically use optimization techniques such as the method of Lagrange multipliers, where the constraint is incorporated into the objective function to form a new function to be maximized or minimized.### Graphs/DiagramsThere are no specific graphs or diagrams provided in the problem. However, if visual aids were to be included:- **Graph of the Constraint Line \( x + y = 2 \)**: A straight line in the \( xy \)-plane, where for each \( x \), \( y \) is determined such that the sum of \( x \) and \( y \) equals 2. - **Graph of the Circular Boundary \( 18 - x^2 - y^2 = 0 \)**: A circle centered at the origin with a radius of \( \sqrt{18} \) (since \( x^2 + y^2 = 18 \)).Combining these, one could plot the circle and the line to find the feasible region and then determine the maximum value of the function within this region.

Name: ### Problem Statement**Objective:** Maximize the function \( f(x, y)
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: ### Problem Statement**Objective:** Maximize the function \( f(x, y) = \sqrt{18 - x^2 - y^2} \).**Subject to the constraint:** \( x + y - 2 = 0 \).### ExplanationIn this problem, we are provided with a multivariable function \( f(x, y) \), which we