For a concert, there are $50 reserved seat tickets and $35 general admission tickets. there are 2000 reserved seats available, and the fire code limits the total number of audience members to 3000. the promoter must take in $90,000 in ticket sales to break even. find a system of five inequalities that represents this problem. (let x for the number of general admission tickets and y represent the number of reserved seat tickets. enter your answers as a comma-separated list of inequalities.)

Question

Mathematics

Heidy

12 September, 19:45

For a concert, there are $50 reserved seat tickets and $35 general admission tickets. there are 2000 reserved seats available, and the fire code limits the total number of audience members to 3000. the promoter must take in $90,000 in ticket sales to break even. find a system of five inequalities that represents this problem. (let x for the number of general admission tickets and y represent the number of reserved seat tickets. enter your answers as a comma-separated list of inequalities.)

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Miah Castillo · Answer 1

The number of seats sold cannot be negative, so you have

... x ≥ 0, y ≥ 0

The limits on numbers of seats must be observed, so you have

... y ≤ 2000

... x + y ≤ 3000

And the revenue constraint must be met:

... 35x + 50y ≥ 90,000

Together, these inequalties are ...

{x ≥ 0, y ≥ 0, y ≤ 2000, x + y ≤ 3000, 35x + 50y ≥ 90,000}