Finding Optimal Panel Dimensions to Minimize Total Area

[sharklaser]

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.

 

[HallsofIvy]

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!