Answer:
6.84 ≤ x ≤ 37.39
Step-by-step explanation:
we have
[tex]P(x)=-0.5x^2+23x+92[/tex] -----> equation A
we know that
The company wants to keep its profits at or above $225,000,
so
[tex]PXx)\geq 225[/tex] -----> inequality B
Remember that P(x) is in thousands of dollars
Solve the system by graphing
using a graphing tool
The solution is the interval [6.78,39.22]
see the attached figure
therefore
A reasonable constraint for the model is
6.84 ≤ x ≤ 37.39