At an amusement park there's only enough room for 4500 people to be in it at any time. The manager has also worked out that there needs to be 2800 people in the park to make a profit after all the overhead costs and employee pay. If people are entering the park at a rate of 12 people a minute and there are 850 people in the park currently between how many minutes should the door stay open to let guests in? (a) Translate the scenario above into a compound inequality involving the number of minutes, m, that the door has been open. Take into account both the fact that there must be a minimum of 2800 people and a maximum of 4500 people.
(b) Rewrite the inequality you found in part (a) using the AND connector and then solve the compound inequality.
(c) Write a solution set as a single statement using interval notation.