Need help with this

[Sheddy225]

I’ve tried multiple times and keep getting each step of the way wrong I only get 2 attempts and then I get new numbers

[Baltuilhe]

Good morning!

Cost:
[tex]C(x)=2x+26[/tex]
Price:
[tex]p(x)=30-2x[/tex]
R(x):
[tex]R(x)=xp(x)=x(30-2x)=30x-2x^2[/tex]

Calculating the profit function:
[tex]P(x)=R(x)-C(x)=30x-2x^2-(2x+26)\\P(x)=-2x^2+28x-26[/tex]

To maximize profit:
[tex]P'(x)=0\\-4x+28=0\\x=7[/tex]

Max-Profit:
[tex]P(7)=-2(7)^2+28(7)-26=-2(49)+196-26=72[/tex]

I hope I have helped!