Profit is the difference between revenue and cost.
The profit reduces by #40, when production increases from 120 to 122
The given parameters are:
[tex]\mathbf{C(x) = 400 + 4x}[/tex]
[tex]\mathbf{R(x) = 30x - \frac{x^2}{40}}[/tex]
The profit function is:
[tex]\mathbf{P(x)=R(x) - C(x)}[/tex]
So, we have:
[tex]\mathbf{P(x)=400 + 4x - 30x + \frac{x^2}{40}}[/tex]
[tex]\mathbf{P(x)=400 - 26x + \frac{x^2}{40}}[/tex]
Differentiate
[tex]\mathbf{P'(x)=- 26 + \frac{2x}{40} \Delta x}[/tex]
Where:
[tex]\mathbf{\Delta x = x_2 - x_1}[/tex]
[tex]\mathbf{x = x_1 = 120}[/tex]
[tex]\mathbf{x_2 = 122}[/tex]
So, we have:
[tex]\mathbf{P'(x)=(- 26 + \frac{2 \times 120}{40}) (122 - 120)}[/tex]
[tex]\mathbf{P'(x)=(- 26 + 6) (122 - 120)}[/tex]
[tex]\mathbf{P'(x)=-40}[/tex]
So, the profit reduces by #40, when production increases from 120 to 122
Read more about profit functions at:
https://brainly.com/question/18714546
