You are making some cakes to sell and want to maximize your profits. You bake two varieties of cake: chocolate cake and carrot cake. Chocolate cake has a profit of $6 a cake, and carrot cake has a profit of $7 a cake.
Both types of cake use general baking supplies. You have 16 of these supplies. Each chocolate cake uses 1 supplies, and each carrot cake uses 2 supplies. Furthermore, you have enough cocoa for 6 chocolate cakes, and you have enough carrots for 6 carrot cakes.
Let a be the number of chocolate cakes produced and sold, and let y be the number of carrot cakes produced and sold. Let P represent the profits from selling the cakes.
1. (5pts) Write out an objective function that determines the profits P in terms of a
2. (5pts) List out the 5 constraints for this problem.
3. (5pts) Graph the constraints, and shade in the feasible region.
4. (5pts) Determine the vertices, and then use them to find the maximum profit