Lagrange Multipliers: determine dimensions of a rectangular box
- Thread starter odat
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- Nov 24, 2012
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Hello, and welcome to FMH! 
I would begin be letting the dimensions of the box be:
[MATH]L[/MATH] = length
[MATH]W[/MATH] = width
[MATH]H[/MATH] = height
Next, I would determine the objective function, that is, the function we wish to optimize. The amount of material needed to construct the box, assuming uniform thickness (which we can ignore), is equal to the outer surface area of the box. Can you construct this function representing the area of the bottom and the 4 vertical sides as a function of the 3 variables above?
I would begin be letting the dimensions of the box be:
[MATH]L[/MATH] = length
[MATH]W[/MATH] = width
[MATH]H[/MATH] = height
Next, I would determine the objective function, that is, the function we wish to optimize. The amount of material needed to construct the box, assuming uniform thickness (which we can ignore), is equal to the outer surface area of the box. Can you construct this function representing the area of the bottom and the 4 vertical sides as a function of the 3 variables above?