A small pottery is setting up a workshop to produce mugs. Three machines are located on a long table, as shown in the figure. The potter must use each machine once in the course of producing a mug. Let x
represent the coordinate of the potter’s station.
pottery workshop
Write expressions for the distance from the potter’s station to each of the machines.
Distance to left-most machine:
abs(x+12)
Distance to middle machine:
abs(x+4)
Distance to right-most machine:
abs(x-24)
Write a function that gives the sum of the distances from the potter’s station to the three machines.
f(x)=

x+40
Graph your function for −20≤x≤30
. Where should the potter stand in order to minimize the distance she must walk to the machines?
Answer: at x
-coordinate