Final answer:
Graph a linear system for Midway High School's musical revenue where student tickets cost $7 and adult tickets cost $12. The graph displays the production cost line and seating capacity line intersecting to form the feasible region for profitability.
Step-by-step explanation:
The question involves creating a graph for a linear system that represents ticket sales for a spring musical at Midway High School. To earn a profit on the production costs of $1900, the school must sell tickets to fill the auditorium, which seats 200 people. With student tickets priced at $7 and adult tickets at $12, the equations for the system are 7y + 12x ≥ 1900 (to cover costs) and x + y ≤ 200 (to account for seating capacity). The graph would include two lines, one representing the cost equation and one representing the seating limit. The solution region is where both inequalities intersect and it's the area where the number of different types of tickets sold results in a profit without exceeding the seating capacity. To graph the system, we plot two lines based on the given inequalities. The line for 7y + 12x = 1900 represents the break-even point for ticket sales, while the line for x + y = 200 represents the maximum number of tickets that can be sold. The solution region is the intersection of the regions where both inequalities are satisfied. The graph should be labeled with axes representing the number of adult (x) and student (y) tickets. The region that satisfies both conditions is where the school will earn a profit and not exceed the auditorium's seating limit.