Question $2(16$ marks$)$

A building's HVAC $($Heating$,$ Ventilation, and Air Conditioning$)$ system need to distribute air to three different zones. The airflow requirements for each zone are as follows:

$-$ zone $1$: $300$ cubic feet per minute $($CFM$)$

$-$ zone $2$: $450$ CFM

$-$ zone $3$: $400$ CFM

The system has three ducts, each with different airflow capacities. The airflow distribution matrix is given as follows:

Table Q$2$ Airflow Distribution Matrix

$($i$)$ Write three equations of each zone according to the airflow matrix. Find the airflow capacities of the three ducts if the airflow requirement is fulfilled.

$($ii$)$ Use MATLAB or Octave to find the airflow capacities by showing the steps in details.