The domain when the maximum number of people allowed in the movie theater is 50 people is:
40 ≤ y ≤ 140
The graph is given as follows:
[tex]y=2x+40[/tex]
where x represent the number of people and y represent the amount of money.
Now, it is given that:
A maximum umber of people allowed in the movie theater is 50 people.
i.e. the inequality which describes this situation is:
[tex]x\leq 50[/tex]
Also,
[tex]0\leq x[/tex]
Hence, we have:
[tex]0\leq x\leq 50[/tex]
i.e.
[tex]2\times 0\leq 2\times x\leq 2\times 50\\\\i.e.\\\\0\leq 2x\leq 100\\\\i.e.\\\\0+40\leq 2x+40\leq 100+40\\\\i.e.\\\\40\leq 2x+40\leq 140[/tex]
i.e.
[tex]40\leq y\leq 140[/tex]
Hence, the domain is:
40 ≤ y ≤ 140
