Question

In: Statistics and Probability

Use Lagrange multipliers to solve the given optimization problem. HINT [See Example 2.] Find the minimum...

Use Lagrange multipliers to solve the given optimization problem. HINT [See Example 2.] Find the minimum value of f(x, y) = x2 + y2 subject to x + 2y = 45.

fmin =

Also find the corresponding point (x, y). (x, y) =

Expert Solution

Using the lagrange multiplier method, we minimize the value of the given function here as:

The lagrange function is given as:

Where C(X, Y) is the constraint here.

Finding the partial derivatives here:

Putting in terms of we get here:

Therefore, we have here the point as:

Therefore, f_min = x² + y² = 9² + 18² = 405

therefore 405 is the required minimum function value here.

Also as already computed above, the corresponding point here is ( 9, 18)

orchestra answered 2 years ago

2.) Use the method of Lagrange multipliers to find the maximum and minimum values of the...

2.) Use the method of Lagrange multipliers to find the maximum and minimum values of the function ?(?, ?) = ??^2 − 2??^2 given the constraint ?^2 + ?^2 = 2 along with evaluating the critical points of the function, find the absolute extrema of the function ?(?, ?) = ??^2 − 2??^2 in the region ? = {(?, ?)|?^2 + ?^2 ≤ 2}.

use Lagrange multipliers to find the maximum and minimum values of f subject to the given...

use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. f(x, y, z) = xyz, x2 + y2 + 4z2 = 12

Use the method of Lagrange multipliers to find the absolute maximum and minimum values of the...

Use the method of Lagrange multipliers to find the absolute maximum and minimum values of the function f(x, y, z) = x^2yz^2 subject to the constraint 2x ^2 + 3y^ 2 + 6z^ 2 = 33

use the method of Lagrange multipliers to find the absolute maximum and minimum values of the...

use the method of Lagrange multipliers to find the absolute maximum and minimum values of the function subject to the given constraints f(x,y)=x^2+y^2-2x-2y on the region x^2+y^2≤9 and y≥0

Use Lagrange multipliers to find the point on the given plane that is closest to the...

Use Lagrange multipliers to find the point on the given plane that is closest to the following point. x − y + z = 6; (2, 7, 3)

Use Lagrange multipliers to find the distance from the point (2, 0, −1) to the plane...

Use Lagrange multipliers to find the distance from the point (2, 0, −1) to the plane 4x − 3y + 8z + 1 = 0.

Use Lagrange multipliers to find the point on the plane 2x + y + 2z =...

Use Lagrange multipliers to find the point on the plane 2x + y + 2z = 6 which is closest to the origin

Use the method of Lagrange multipliers to find the extreme values of f(x, y) = 2x^2−3y^2...

Use the method of Lagrange multipliers to find the extreme values of f(x, y) = 2x^2−3y^2 subject to the constraint that x^2+y^2 = 3.

Use Lagrange Multipliers to find any max or min values of f(x,y) = y^2 - 7x^2...

Use Lagrange Multipliers to find any max or min values of f(x,y) = y^2 - 7x^2 with the constraint x^2 + 2y^2 = 4

Use Lagrange multipliers to find the maximum production level when the total cost of labor (at...

Use Lagrange multipliers to find the maximum production level when the total cost of labor (at $111 per unit) and capital (at $50 per unit) is limited to $250,000, where P is the production function, x is the number of units of labor, and y is the number of units of capital. (Round your answer to the nearest whole number.) (Please use the numbers given I've followed other 'solutions' and keep getting the wrong answer, I just want to see...