Answer:
The company's maximum monthly profit is $18050
Step-by-step explanation:
First we need to distribute everything in order to solve for the maximum
[tex]f(x)=-2(x-10)(x-200)\\\\f(x)=-2(x^2-210x+2000)\\\\f(x)=-2x^2+420x-4000[/tex]
Now we can use the equation [tex]x=\frac{-b}{2a}[/tex] in order to find the x-value of the maximum
From our function, we know that a=-2 and b=420
We can plug in these values and solve for x to get
[tex]x=\frac{-420}{-2(2)} \\\\x=\frac{420}{4} \\\\x=105[/tex]
Now we can plug our x-value into our function in order to find the maximum monthly profit
[tex]f(x)=-2x^2+420x-4000\\\\f(105)=-2(105)^2+420(105)-4000\\\\f(105)=-2(11025)+44100-4000\\\\f(105)=-22050+44100-4000\\\\f(105)=18050[/tex]
