Thomas and Theresa work for a company that receives $75 for each unit of output sold. The company has a variable cost of $30 per item and a fixed cost of $12,000.

Based on this information, Thomas and Theresa make some projections about potential profit.

Thomas states that for every 500 units of output sold, the company will make $11,000 in profit.
Theresa states that for every 800 units of output sold, the company will make $24,000 in profit.

Determine a function that models the profit for the company based upon the conditions for revenue and expense.
Are the claims about profit that Thomas and Theresa made true? Explain why Thomas and Theresa are each correct or incorrect and justify your reasoning.