A delivery business plans to serve three towns on a stretch of highway. For every trip they make to town A, which we'll place at position x=0, they expect to make two trips to town B (at position x=1) and 3 trips to town C (at position x=4). If they build their delivery centre at position x, then, their daily driving time should be proportional to d(x) = |x| + 2|x - 1| + 3|x - 4|. The owners are thinking of building the center in town C, since it's the biggest but overhead costs would be lower in town B. Where should they build?

Question

A delivery business plans to serve three towns on a stretch of highway. For every trip they make to town A, which we'll place at position x=0, they expect to make two trips to town B (at position x=1) and 3 trips to town C (at position x=4). If they build their delivery centre at position x, then, their daily driving time should be proportional to d(x) = |x| + 2|x - 1| + 3|x - 4|. The owners are thinking of building the center in town C, since it's the biggest but overhead costs would be lower in town B. Where should they build?
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Well, I think I should sketch the function too, but I don't know how...
Thanks for any help.

MathMate · Answer

Using the function
d(x) = |x| + 2|x - 1| + 3|x - 4|
make a table of values of
x and d(x)
for x = 0, x=1 and x=4.

If the company decides to build the delivery centre along a highway, then intermediate values of x should also be considered.

I have an impression that the owners will have quite a fight over the location.

Tell me what you think.