x - number of games
22x - cost of x tickets
10 - parking cost
The equation:
The town librarian bought a combination of new-release movies on DVD for $20 and classic movies on DVD for $8. Let x represent t
1 answer:
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Notice that
so the constraint is a set of two lines,
and only the first line passes through the first quadrant.
The distance between any point in the plane is
, but we know that
and
share the same critical points, so we need only worry about minimizing
. The Lagrangian for this problem is then
with partial derivatives (set equal to 0)
We have
which tells us that
so that is a critical point. The Hessian for the target function
is
which is positive definite for all , so the critical point is the site of a minimum. The minimum distance itself (which we don't seem to care about for this problem, but we might as well state it) is
.
This is something you'll need a T table for, or a calculator that can compute critical T values. Either way, we have n = 10 as our sample size, so df = n-1 = 10-1 = 9 is the degrees of freedom.
If you use a table, look at the row that starts with df = 9. Then look at the column that is labeled "95% confidence"
I show an example below of what I mean.
In that diagram, the row and column mentioned intersect at 2.262 (which is approximate). This value then rounds to 2.26
<h3>Answer: 2.26</h3>