From the given equation we get that the optimal time is represented by the following inequality:
[tex]|100t-1200|\le200.[/tex]
Now, recall that:
[tex]\begin{gathered} |a|\leq b\text{ if and only if } \\ -b\leq a\leq b\text{.} \end{gathered}[/tex]
Therefore:
[tex]-200\le100t-1200\le200.[/tex]
adding 1200 to the above inequality, we get:
[tex]1000\le100t\le1400.[/tex]
Finally, dividing by 100 we get:
[tex]10\le t\le14.[/tex]
Answer: The time interval is between 10 and 14 days.
