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Let's come back to the idea of contour
lines, shown here in dashed blue lines.

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Contour lines are lines that show equal height.

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If you walk along a contour line, you are
not going up and you are not going down.

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Here's a photo of Mount Fuji in
Japan on the left, and a contour plot

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of the mountain is shown on the right.

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Notice that these small numbers here on the
plot tell how high up the mountain we are.

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Response surface methods can be thought of, at
least conceptually, using the following analogy.

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Imagine you're in a basement in someone
else's house and the lights suddenly go out.

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You grab a ski pole and start to tap the
ground to test the slope of the floor.

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You know that the door is the highest point in
the basement and you want to reach that door.

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Now also imagine that you want to reach

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that point using the minimum number
of taps -- for whatever reason.

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This is exactly how we treat
response surface methods.

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The objective is to find the maximum
on the contour plot using that pole.

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Each time you touch the surface, you're
observing the system and get an outcome value.

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But when you do that, it is
a really expensive process.

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Each time you touch the surface or run an
experiment, it might cost hundreds of dollars.

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How do you get to that optimum efficiently?

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How do you know that you've reached the optimum

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with only the information
from the taps of the pole?

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Remember the lights are out, so
you cannot see what's around you.

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That's what the videos in the section are
all about, getting to the top of that surface

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with as few uses of that ski pole as possible.

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People often ask, what should
this mountain surface look like?

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What does it consist of?

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Well, it is usually your outcome variable,
something like total sales that you want

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to maximize, or the number of unburned popcorn,
or the height of plants that you are growing.

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If you're ever stuck thinking
about which variable

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to maximize, you should consider profit.

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Profit is a good choice because it includes
the income and accounts for all the expenses.

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Let me give you an example.

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In many engineering systems,
we can make things faster

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by increasing the temperature,
but that energy is not free.

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As we go to higher and higher temperature

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and make things faster, our
costs are also increasing.

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The calculated value of profit takes all
of those into account in a single number.

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You'll find that profit, as an outcome
variable, often has the shape of a mountain.

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It is a great way to incorporate multiple
objectives into a single quantity.

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More on that in the next video.

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Now, you don't always have
to climb the mountain.

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Sometimes you want to be in the
valley and get the minimum value.

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Consider the wastewater treatment
example from earlier in the course.

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We wanted to minimize the amount of pollution.

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In this course, all our examples
will be for maximizing,

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but minimizing is just the
opposite of maximizing.

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In fact, those with a background
in optimization theory will know

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that maximization is just
the negative of minimization.

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For example, in the waste water problem, if
we tried to maximize the negative pollution,

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that is the same as minimizing pollution.

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Now I'll wrap up this video and leave
you with some questions to think about.

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How do we climb up that mountain?

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Which direction should we go up
and how big should our steps be?

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How do we handle nonlinear
surfaces as we climb up?

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When do we stop?

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Because remember, we don't have a contour
map, so we need to have a way to know

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that we've really reached the peak.