(Solved): 1. A corporation has two industrial plants \( \mathrm{A} \) and \( \mathrm{B} \) located \( 18 \ma ...

1. A corporation has two industrial plants \( \mathrm{A} \) and \( \mathrm{B} \) located \( 18 \mathrm{~km} \) apart. Each day plant A emits \( 80 \mathrm{ppm} \) (parts per million) of a particulate matter and plant B emits \( 720 \mathrm{ppm} \) of the same particulate matter. Plant \( \mathrm{A} \) is surrounded by a restricted area of radius \( 1 \mathrm{~km} \), in which no housing is allowed, while the restricted area around plant B has a radius of 2 \( \mathrm{km} \). Environmentalists estimate that the concentration of particle matter arriving at any other point \( Q \) from each plant decreases proportional to the reciprocal of the distance between that plant and \( Q \). If the corporation would like to build a headquarter building on a straight road joining the plants \( \mathrm{A} \) and \( \mathrm{B} \), where should the building be located to minimize the total concentration of the particulate matter arriving from both plants? Calculate the total concentration of the particulate matter that would be arriving to the headquarter from both plants.