The area of a triangle with sides of length a, b, and c is √(s(s-a)(s-b)(s-c)), where s is half the perimeter of the triangle. We have 60 feet of fence and want to fence a triangular-shaped area. Part A: Formulate the problem as a constrained nonlinear program that will enable us to maximize the area of the fenced area, with constraints. Clearly indicate the variables, objective function, and constraints.

Hint: The length of a side of a triangle must be less than or equal to the sum of the lengths of the other two sides.

Part B: Solve the Program (provide exact values for all variables and the optimal objective function). Use Python to solve this problem.