Answer:
Therefore, the average change in revenue when the firm increases sales from 30 to 35 units is $70.
Step-by-step explanation:
AI-generated answer
To find the average change in revenue when the firm increases sales from 30 to 35 units, we need to calculate the change in revenue and then find the average change.
Given the revenue function:
\( R(q) = 200q - 2q^2 \)
Let's find the revenue at q = 30 and q = 35:
1. Revenue at q = 30:
\( R(30) = 200(30) - 2(30)^2 = 6000 - 1800 = 4200 \)
2. Revenue at q = 35:
\( R(35) = 200(35) - 2(35)^2 = 7000 - 2450 = 4550 \)
Now, calculate the change in revenue:
\( Change\ in\ revenue = R(35) - R(30) = 4550 - 4200 = 350 \)
To find the average change in revenue, divide the change in revenue by the increase in sales (from 30 to 35 units):
\( Average\ change\ in\ revenue = \frac{Change\ in\ revenue}{Change\ in\ sales} = \frac{350}{35-30} = \frac{350}{5} = 70 \)
