A bakery is making apple pies and carrot cakes. Each
apple pie nets $5 profit. For each carrot cake, they
make $10 profit. Each pie take 4 hours to prepare and
1.5 hours to bake. The carrot cakes take 0.5 hours to
prepare and 0.5 hours to bake. The maximum
preparation time is 20 hours. The maximum baking
time is 10 hours. How many pies and cakes should be
made to maximize profits?