Problem: Design a cylindrical tank closed at both ends to have a volume of 300 m3. The fabrication cost is proportional to the surface area of the sheet metal and is $900/m2. The tank is to be housed in a shed with a sloping roof. Therefore, the height, H, of the tank is limited by the relation12 /2 -H D, where D is the diameter of the tank. Formulate the minimum cost design problem.
(a) Formulate the problem.
(b) Solve the problem utilizing the methods of Chapter 4
(c) Verify your solution graphically
(d) Which constraints (if any) are active?
(I would suggest working in units of $1,000 for the cost function.)