U = b + 100c - c^2 where b is the number of peppers and c is the number of carrots. There are 500 square feet in the garden. Peppers each take up 1 square foot and carrots each take up 4 square feet. Seeds are free, and each takes the same level of effort and time to plant.

(a) To maximize Utility, How many peppers and carrots should be planted? Show work.

(b) If an extra 100 square feet was added to the garden, how much should the planting of each item increase? Explain.

(c) If we did not know how large the garden was, but we do know both carrots and peppers are planted: Can we determine either a minimum or maximum size for the garden? Explain.