i need help with a linear programming word problem.?

Question

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?

Answer 1

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 <= 18,000
p<=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>=5000. So from that standpoint it's a bit of a trick question.

Answer 2

s ≥ 5000
s+p ≤ 18000
Solve for p,
p ≤ 18000 - 5000 = 13000