The client wants to maximise the volume of a materials store to be constructed next to a 3 metre high stone wall (shown as OA in the cross section in the diagram). The roof (AB) and front (BC) are to be constructed from corrugated metal sheeting. Only 6 metre length sheets are available. Each of them is to be cut into two parts such that one part is used for the roof and the other is used for the front. Find the dimensions x and y of the store that will maximise the cross‐sectional area and therefore the volume. Hence determine the maximum cross‐sectional area. 
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$\begingroup$ Please help! This assignment is due tomorrow! $\endgroup$– RachelJul 21, 2014 at 0:53
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$\begingroup$ Can you give a picture ? $\endgroup$– Tony PiccoloJul 21, 2014 at 8:04
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$\begingroup$ @TonyPiccolo The image has been added $\endgroup$– RachelJul 21, 2014 at 9:58
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1 Answer
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Hint:
By Pythagoras find $y$ as a function of $x$ (squaring the constraint side by side) and then optimize the area as a function of $x$.
answered Jul 21, 2014 at 23:22