Originally Posted by

**jjoechump** Ok so this one is hanging me up...

Two industrial plants, A and B, are located 20 miles apart and emit 40 ppm (parts per million)

and 90 ppm of particulate matter, respectively. Each plant is surrounded by a restricted area

of radius 1 mile in which no housing is allowed and the concentration of pollutant arriving at

any other point Q from each plant decreases with the reciprocal of the distance between that

plant and Q. A warehouse need to be built on a road joining the two plants.

a) Lets say the house is located x miles from plant A (and hence 20 – x from plant B). Express

the total concentration of particulate matter arriving from both plants. What is the condition

on x?

b) Where should the house be located on the road to minimize the total pollution arriving

from both plants? (That is, find x to minimize the function you have in question a )