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The function f(x) = –(x – 20)(x – 100) represents a company’s monthly profit as a function of x, the number of purchase orders received. Which number of purchase orders will generate the greatest profit?
20
60
80
100

Respuesta :

60 would produce the greatest profit of 1,600.

If correct brainiest please

Thank you

:)

Answer:

The correct option is 2.

Step-by-step explanation:

The given function is

[tex]f(x)=-(x-20)(x-100)[/tex]

It can be written as

[tex]f(x)=-x^2+120x-2000[/tex]           .... (1)

It is a downward parabola because the leading coefficient is negative. The value of the parabola is maximum at its vertex.

If a parabola is define as

[tex]p(x)=ax^2+bx+c[/tex]               .... (2)

then it is maximum at [tex]x=\frac{-b}{2a}[/tex].

From (1) and (2), we get

[tex]a=-1,b=120,c=-2000[/tex]

The profit is maximum at

[tex]x=\frac{-120}{2(-1)}=60[/tex]

Therefore the profit is maximum when the number of purchase orders is 60. Option 2 is correct.

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