The model

$\displaystyle y=80.4 - 11\ln x$, $\displaystyle 100\leq x\leq 1500$

which approximates the minum required ventilation rate in terms of the air space per child in a publich classroom. In the model, $\displaystyle x$ is the air space per child in cubic feet and $\displaystyle y$ is the ventilation rate per child in cubic feet per minute.

A classroom is designed for 30 students. The air conditioning system in the room has the capacity of moving 450 cubic feet of air per minute.

(a) Determine the ventilation rate per child, assuming that the room is filled to capacity.

(b) Estimate the air space require per child.

(c) Determine the mininum number of square feet of floor space required for the room if the ceiling height is 30 feet.