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So for those of you in Econ 150,
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this should be a very familiar kind of thing.
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This is a constrained optimization problem
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and you've been having constrained optimization problems
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rammed into you for the last month or so,
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so this is an example of a constrained optimization problem.
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You have to choose a point
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but you can't choose a point freely:
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you have to choose a point on the line.
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Okay, so let's talk about it a bit more before we do the math.
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Let's actually redraw it again
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since I made a mess of this picture.