3. Donald plans to bake and sell cakes. The three types of cake that he can bake are brownies, flapjacks and muffins. Donald decides to bake 48 brownies and muffins in total.
Donald decides to bake at least 5 brownies for every 3 flapjacks.
At most \(40 \%\) of the cakes will be muffins.
Donald has enough ingredients to bake 60 brownies or 45 flapjacks or 35 muffins.
Donald plans to sell each brownie for \(\pounds 1.50\), each flapjack for \(\pounds 1\) and each muffin for \(\pounds 1.25\) He wants to maximise the total income from selling the cakes. Let \(x\) represent the number of brownies, let \(y\) represent the number of flapjacks and let \(z\) represent the number of muffins that Donald will bake. Formulate this as a linear programming problem in \(x\) and \(y\) only, stating the objective function and listing the constraints as simplified inequalities with integer coefficients. You should not attempt to solve the problem.