Who's smart enough to solve this?

Question

WARNING: It's hella hard.

2 students are organizing the high school prom. They are selling 2 tickets- individual tickets and couples tickets. The room where the prom is hold 400 max.

The two students think the prom will be more successful when more people go as couples. So at least half the people at the prom will be couples, they decide that the number of individual tickets sold should be at most twice the number of couples.

Unfortunately, they only have 225 tickets to sell. So they can sell a total at most 255 tickets.

a) Suppose individual tickets sell for $22 and couples sell for $30. How many of each type of tickets should they sell to maximize the money they get?

b) Same as above but, individual- $15 and couples- $35

c) Same as above but, individual- $30 and couples- $20.

I need to find the constraints and the teacher told us to graph it...how do I do that? And is that all I have to do? Can you please explain and solve this thoroughly so I can understand so I won't look like an idiot?

Answer 1

x = INDIVIDUAL TICKETS

y = COUPLES TICKETS

CONSTRAINT 1

2x ≤ y (“they decide that the number of individual tickets sold should be at most twice the number of couples”)

CONSTRAINT 2

x + y = 225  (“they only have 225 tickets to sell”)

a) SALES = x * 22 + y * $30

b) SALES = x * 15 + y * $35

c) SALES = x * 30 + y * $20