what you do first is you times the F which will equal -2 which will give you an answer then you subtract that answer by 10 * by 200 than you have your answer
Answer:
The maximum monthly profit is 18050.
Step-by-step explanation:
The given function is
[tex]f(x)=-2(x-10)(x-200)[/tex]
[tex]f(x)=(-2x+20)(x-200)[/tex]
[tex]f(x)=-2x(x-200)+20(x-200)[/tex]
[tex]f(x)=-2x^2+400x+20x-4000[/tex]
[tex]f(x)=-2x^2+420x-4000[/tex] .... (1)
The vertex of a quadratic function
[tex]g(x)=ax^2+bx+c[/tex] ..... (2)
is defend as
[tex](\frac{-b}{2a},f(\frac{-b}{2a}))[/tex]
From (1) and (2) we get
[tex]a=-2,b=420,c=-4000[/tex]
[tex]\frac{-b}{2a}=\frac{-420}{2(-2)}=105[/tex]
Put x=105 in the given function.
[tex]f(105)=-2(105-10)(105-200)[/tex]
[tex]f(105)=-2(95)(-95)[/tex]
[tex]f(105)=18050[/tex]
Therefore the maximum monthly profit is 18050.
