LifeTrace is a very successful social media and business consulting firm. Several times each quarter, the company pays for each employee’s one-hour massage and a one-hour personal training session at a local gym, depending on the day and the employee’s preference. Each massage costs $40, while each personal training session costs $30. However, the company’s total cost for providing these services cannot exceed $6,550.00 per quarter.

The following inequality represents the amount of money that LifeTrace spends on massages and personal training sessions.

40x + 30y ≤ $6550

Part A: Determine the domain for variable x.

Part B: Determine the range for variable y.

Part C: This past year, LifeTrace provided 100 massages and 83 personal training sessions during the first quarter and 67 massages and 130 personal training sessions during the second quarter. Did the company exceed its quarterly budget at any point? Justify your answer.