Using an linear function, we have that:
- The inequality is: [tex]-150D + 7250 < 2000[/tex]
- The warehouse will start printing more books on the 35th day, hence it won't be printing on the 30th day.
What is a linear function?
A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
In this problem:
- A warehouse contains 7250 books in it, hence b = 7250.
- Books are being shipped from the warehouse such that the number of books decreased by 150 per day, hence m = -150.
Thus, the number of books each day is modeled by the following function:
[tex]B(D) = -150D + 7250[/tex]
It will begin to print more books when the warehouse contains less than 2000 books, hence, the inequality is:
[tex]B(D) < 2000[/tex]
[tex]-150D + 7250 < 2000[/tex]
Then:
[tex]-150D < -5250[/tex]
[tex]150D > 5250[/tex]
[tex]D > \frac{5250}{150}[/tex]
[tex]D > 35[/tex]
The warehouse will start printing more books on the 35th day, hence it won't be printing on the 30th day.
More can be learned about linear functions at https://brainly.com/question/24808124
