Question

the equation that represents the proper traffic control and emergency vehicle response availability in a small city is 2p + 3f ≤ 23, where p is the number of police cars on active duty and f is the number of fire trucks that have left the firehouse in response to a call. in order to comply with staffing limitations, the equation 4p + 2f ≤ 34 is appropriate. the number of police cars on active duty and the number of fire trucks that have left the firehouse in response to a call cannot be negative, so p ≥ 0 and f ≥ 0. graph the regions satisfying all the availability and staffing requirements, using the horizontal axis for p and the vertical axis for f. if 5 police cars are on active duty and 5 fire trucks have left the firehouse in response to a call, are all of the requirements satisfied?

Explanation:

Step1: Check the first inequality

Substitute \(P = 5\) and \(F=5\) into \(2P + 3F\leqslant23\).
\[2\times5+3\times5=10 + 15=25\]
Since \(25>23\), \(2P + 3F\leqslant23\) is not satisfied.

Step2: Check the second - inequality

Substitute \(P = 5\) and \(F = 5\) into \(4P+2F\leqslant34\).
\[4\times5+2\times5=20 + 10=30\]
Since \(30\leqslant34\), \(4P + 2F\leqslant34\) is satisfied. But since the first inequality is not satisfied, all requirements are not met.

Answer:

No