In Exercise 31, suppose the concentration of particulate matter arriving at a point Q from each plant decreases with the reciprocal of the square of the distance between that plant and Q. With this alteration, now where should a house be located to minimize the total concentration of particulate matter arriving from both plants?

Data from Exercises 31

Two industrial plants, A and B, are located 18 miles apart, and each day, respectively, emit 80 ppm (parts per million) and 720 ppm of particulate matter. Plant A is surrounded by a restricted area of radius 1 mile, while the restricted area around plant B has a radius of 2 miles. The concentration of particulate matter arriving at any other point Q from each plant decreases with the reciprocal of the distance between that plant and Q. Where should a house be located on a road joining the two plants to minimize the total concentration of particulate matter arriving from both plants?