Design a cylindrical tank closed at both ends to have a volume of 275 m. The fabrication cost is proportional to the surface area of the sheet metal and is $500/m. The tank is to be housed in a shed with a sloping roof. Therefore, the height, H, of the tank is limited by the relation H11-D/2, 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.)