Finding Optimal Panel Dimensions to Minimize Total Area

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SUMMARY

The discussion focuses on optimizing the dimensions of a rectangular catalyst panel that must provide a minimum effective area of 500 cm² while accounting for installation margins of 5 cm on the longer sides and 7 cm on the shorter sides. The optimal panel dimensions are determined to be 50 cm by 70 cm, which minimizes the total area. Participants highlight the importance of formulating a penalty function to address constraints and clarify the relevance of initial guesses in optimization problems.

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A rectangular catalyst panel must provide 500cm2 effective area,
and requires installation margins of 5cm on the longer sides and 7cm
on the shorter sides. What panel dimensions minimize the total area?


(1) Formulate a penalty function, identitfying all constraints(active
and redudant), and confrim that x=50 and y=70 is a suitable initial guess.
 
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This isn't homework? And what in the world does it have to do with differential equations? You are obviously using terms (penalty function, constraints) related to a specific application- don't expect everyone to understand them- define them for us. Finally, why any "initial guess"? This looks to me like an easily solvable problem without any guessing!
 

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