I need help with a linear programming word problem.?

A college arena sells tickets to students and to the public. Student tickets are $8 each and general public tickets are $32 each. The college reserves at least 5,000 tickets for students. The arena seats 18,000.





let s= the # of student tickets


let p= the # of general public tickets





Write a system of inequalities to represent the number of tickets sold.





Can you help me with writing the inequalities?

I need help with a linear programming word problem.?
It's weirdly stated.





Obviously, the objective function is 32p+8s, but the way the problem if phrased that doesn't matter, because money isn't mentioned.





s+p %26lt;= 18,000


p%26lt;=13,000





Those are the only things you know about ticket quantities.





You don't actually know that 5,000 student tickets will be sold, so it's not accurate to say s%26gt;=5000. So from that standpoint it's a bit of a trick question.
Reply:s ≥ 5000


s+p ≤ 18000


Solve for p,


p ≤ 18000 - 5000 = 13000