Chapter 3, Problem 22PS

(a)

To determine

Determine the ventilation rate per child in a full classroom.

Answer to Problem 22PS

The ventilation rate per child $15$ cubic feet per minute

Explanation of Solution

Given:

The room with a capacity of 30 students

  $y=80.4-11\ln x,100\le x\le 1500$

Consider the room with a capacity of 30 students. The air conditioning system has the capacity of moving 450 cubic feet per minute.

Therefore, the ventilation rate per child

  $=\frac{450}{30}$

  $=15$ cubic feet per minute

(b)

To determine

Estimate the air space required per child.

Answer to Problem 22PS

The air space required per child $382.013\text{cubic feet}$

Explanation of Solution

Given:

  $y=80.4-11\ln x,100\le x\le 1500$

Now, according to the model,

  $\begin{array}{cc}y& =80.4-11\ln x\\ 11\ln x& =80.4-y\\ \ln x& =\frac{80.4-y}{11}\\ x& =e^{\frac{80.4-y}{11}}\end{array}$

Therefore, when the ventilation rate

  $y=15$

then the air space required per child

  $\begin{array}{cc}x& =e^{\frac{80.4-15}{11}}\\ & =e^{\frac{65.4}{11}}\\ & =e^{5.945}\\ & =382.013\text{cubic feet}\end{array}$

(c)

To determine

Determine the minimum number of floor space required if the ceiling height is 30 feet.

Answer to Problem 22PS

The floor pace required if the ceiling height is 30 feet is,

  $382.013\text{square feet}$

Explanation of Solution

Given:

The room with a capacity of 30 students

  $y=80.4-11\ln x,100\le x\le 1500$

Consider

  $\begin{array}{cc}\text{volume}& =area(\text{height})\\ \text{area}& =\frac{\text{volume}}{\text{height}}\end{array}$

Therefore, the floor pace required if the ceiling height is 30 feet is,

  $\begin{array}{cc}area& =\frac{30(382.013)}{30}\\ & =382.013\text{square feet}\end{array}$