Let x1 represent the number of tickets sold at $25 and let x2 represent the number of tickets sold at $35.
The total number of tickets sold is given by x1 + x2.
The receipts generated by the $25 tickets 25x1.
The receipts generated by the $35 tickets is 35x2.
The total receipts for all of the tickets is given by 25x1 + 35x2.
Number of Tickets Constraint: x1 + x2 = 10,000 Total Receipts Constraint: 25x1 + 35x2 = $275,000 Non-negative Constraints: x1, x2 ≥ 0