A man has a rectangular back yard that is 50 feet wide and 60 feet deep. (See image below.) From the rectangular shape he plans to construct a pool area (the middle section of the model) and a patio area (represented in brown in the model), where the length of the pool area is more than 10 feet, y 10. (The green area in the model represents the remaining portion of the yard not designated for the patio and pool. He can spend at most $15,000 on the project. The patio area must be at least as large as the pool area. The pool area will cost $10 per square foot, and the patio will cost $5 per square foot.