The rate at which the revenue increases per day is given by:
R'(d) = 28,750*d + 18,000
How rapidly is the revenue increasing?
The revenue as a function of the sold units x is:
R(x) = 1000*x - 3x^2
Now, the sales increase at a rate of 25 units per day, then we can write:
x = 120 + 25*d
Replacing that on the revenue equation, we get:
R(d) = 1000*(120 + 25*d) - 3*(120 + 25*d)^2
Derivating with respect to d, we will get:
R'(d) = 1000*25*d + 2*3(120 + 25*d)*25
R'(d) = 25,000*d + 18,000 + 3,750*d
R'(d) = 28,750*d + 18,000
This is the rate at which the revenue increases as a function of d.
If you want to learn more about the rate of change, you can read:
https://brainly.com/question/8728504
