A company makes three types of products: Product 1 sells at $50 per unit, and has a fixed cost of $ 5000, and a variable cost of $30 per unit. Product 2 sells at $40 per unit, and has a fixed cost of $ 3000, and a variable cost of $20 per unit. Product 3 sells at $60 per unit, and has a fixed cost of $ 6000, and a variable cost of $40 per unit. Find a linear objective function for maximizing the profit.