The height of a cylindrical water tank must be at least twice as much as its base diameter. Neither the diameter nor the height can exceed 10 ft. The volume of the tank must be at least 300 ft³. The cost of the elevated structure on which the tank is installed is proportional to the area of the base. The sheet metal cost is $8/ft², and the cost of the supporting structure is $15/ft². Formulate the problem as a mathematical model, and develop a random-walk heuristic to estimate the diameter and height of the tank.