What are the constraints?

the woodward park high school auditorium seats 150 people. admission to the spring play is two dollars for adults and one dollar for students. the drama club is already sold 50 student tickets and the rest are to be sold at the door. how many of each type should be sold for the drama club to earn the maximum amount of money?

 Subject to the constraints:-

, 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 :

Subject to the constraints:-

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 , we get

The maximum amount of money earned by the drama club=50+2(100)=$250

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

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step-by-step explanation: