Gilbert is baking cookies and brownies for a bake sale. It costs him $3 for every batch of cookies he makes and $4 for every batch of brownies he makes. Each batch of cookies takes 2 hours to make, and each batch of brownies takes 1 hour to make. Gilbert has budgeted a total of $100 for expenses and has allowed himself 45 hours to make the cookies and brownies. He makes a profit of $5 for each batch of cookies, and he makes a profit of $4.50 for each batch of brownies. The system of inequalities that represents this situation, {3x+4y≤1002x+y≤45, is shown graphed in the first quadrant with the number of batches of cookies along the x- and the number of batches of brownies along the y-.
The equation p=5x+4.5y represents the profit (p) that Gilbert makes if he sells all his baked goods.

What combination of baked goods allows Gilbert to maximize his profit?