a trough is made from a rectangular strip of metal 50cm wide. the metal is bent at right angles so i

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a trough is made from a rectangular strip of metal 50cm wide. the metal is bent at right angles so it is x centimetres high along two sides. for what value of x is the cross-sectional area a maximum?

Oct 5th, 2014

If the strip of metal 50 cm wide is bent symmetrically so that the side walls of the (open) trough are x cm high, then the width w of the trough is (50 - 2.x) cm and the cross-sectional area A is given by 

A = x.(50 - 2.x) = 50.x - 2.x² 

To determine the optimum value of x, differentiate this equation and set the result to zero ie 

50 - 4.x = 0, or x = 12.5cm 

The base is (50 - 2 x 12.5) = 25 cm, so the optimum cross-sectional area is 12.5 x 25 = 312.5 cm². 

This procedure can be used for much more complicated situations, where the relationship is not so self-evident.

please choose me best thanks

Oct 6th, 2014

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