Day 19 in Mat329

• You have a homework due today.
• Exams are returned
  • Curve: Add three to your raw score, before dividing by 70....
  • The exam
  • The key

Lagrange multipliers are simply means of introducing constraints into an optimization problem. Perhaps the easiest way to think of this is to imagine two surfaces intersecting, and to ask what the largest value of the first function is upon the curve of intersection.

Let's examine Figure 1 on page 981, to get the idea.

The cool thing is that we can introduce a new variable (the Lagrange multiplier), increasing the dimension of our problem; and then solve that higher-dimensional problem using unconstrained optimization (which we just did -- finding maxes and mins).

So we cast the problem into a higher dimension to solve it.

Problems:

• An example: Use Lagrange multipliers to find the maximum and minimum values of $f(x,y)=4x+6y$ subject to the constraint $x^2+y^2=13$.

• Let's look at #48, p. 979, as a Lagrange multiplier problem.

• Examples from the text, including a surprise

• Why don't you try an example: #25