Answer: Subject to the constraints:-
[tex]x\geq50.....(1)\\x+y\leq150............(2)[/tex], where x be the number of students ticket and y be the number of adult tickets.
The maximum amount of money earned by the drama club=50+2(100)=$250
Step-by-step explanation:
Let x be the number of students ticket and y be the number of adult tickets.
Maximize : [tex]x+2y[/tex]
Subject to the constraints:-
[tex]x\geq50.....(1)\\x+y\leq150............(2)[/tex]
Equation(1) is a line parallel to the y axis with point (50,0) on x axis.
In equation(2), at x=0, y=150 and at y=0, x=150
then plot line passing through points (0,150) and (150,0), then shade the portion according to the signs.
From the graph below we can see the feasible solution for the maximum value is at (50,100)
Put x=50 and y=100 in [tex]2x+y[/tex], we get
The maximum amount of money earned by the drama club=50+2(100)=$250
