Hello friends! I had a question about number 7 from section 13.10 in class today and I figured we could all benefit from the answer. Were asked to maximize 2x + 2xy + y along the line 2x + y = 100. Again we see that the Lagrange method is the way to go here (Im going to use the letter L for lambda because computer). We take our partials and end up with the system of equations 2 + 2y = 2L, 2x + 1 = L, and 2x + y = 100. We can solve each of the first equations for x and y (x = (L - 1)/2, y = L-1). This means that y = 2x. Plugging in to our constraint, we see that x = 25 and y = 50. The point (25,50,2600) is therefore the maximum of our function in this situation. Hope this helps!
Posted on: Wed, 12 Mar 2014 03:09:20 +0000
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