Help with an engineering optimization problem?

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SUMMARY

The discussion focuses on optimizing a design problem involving a rectangular plate and circles with given radii (R1, R2, R3, R4). The objective function to minimize is defined as ab - π(R1² + R2² + R3² + R4²), where 'a' and 'b' represent the dimensions of the plate. The participant expresses confusion regarding the constraints necessary for the design, emphasizing the need to consider the relative positions of the circles and their placement within the rectangular plate to minimize scrap material.

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  • Understanding of optimization techniques in engineering design
  • Familiarity with objective functions and constraints in mathematical modeling
  • Knowledge of geometric properties related to circles and rectangles
  • Basic proficiency in calculus for optimization problems
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lilmul123
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Homework Statement



The link to the problem is here: http://i.imgur.com/wyOsoSB.png

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?
 
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yep. good so far. for the constraints.. just think about what you want the stamp to look like. what constraint does this place on the relative positions of the circles to each other, and to the edge of the rectangular plate?
 

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