Fernando builds birdbaths ( \(x\) ) and birdhouses ( \(y\) ). Fernando can make a total of 7 birdbaths and birdhouses per day. A birdbath costs \(\$ 8\) to make, while a birdhouse costs \(\$ 6\) to make. Fernando has \(\$ 48\) to spend on building materials for the day. When he sells them, Fernando makes \(\$ 12\) in profit on a birdbath and \(\$ 9\) in profit on a birdhouse. Determine how many of each Fernando should make to maximize his profit for the day.

Use the four steps for solving linear programming problems to solve.