1. The problem statement, all variables and given/known data The link to the problem is here: http://i.imgur.com/wyOsoSB.png 3. The attempt at a solution I'm not completely sure about my work so far so please bear with me. My professor is very poor at professing the subject so I'm trying to learn from the book. Please let me know if I'm incorrect at any point. I have determined that since R1, R2, R3, and R4 are given, they are not part of the design to be minimized. What matters is the length and height of the plate (a and b) and the location of the origin of each circle (so x1,y1 and x2,y2, etc.). This is where I start to get confused. So the objective function to be minimized would be ab - [ pi(R12 + R22 + R32 + R42 ], correct? Because ideally, we want to have as least amount of scrap as possible? What would be my constraints be?