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

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