Answer:
He can earn $79
Step-by-step explanation:
The maximun benefic that he can earn is represented by the tangent of the function when his value is zero.
Writing the function: P(x)= -[tex]x^{2}[/tex]+12x+43, now we have to derivate
P´(x)= -2x + 12.
To have the maximun profit we do P´(x)=0
0=-2x+12⇒ 2x=12 ⇒ x=12/2 ⇒ x=6
The next step is replace this value on the P(x)
P(6)= -[tex]6^{2}[/tex]+12*6+43
P(6)= $79
