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A person decides to convert their car from petrol to LPG by installing an LPG tank in their boot. In order for the change to be viable the size of the tank needs to be maximised. The tank must be cylindrical in shape, with the net of the tank being cut from a single piece of steel 240cm x 190 cm and can be made using portrait (widthwise) or landscape (lengthwise) orientation. Note: the ends will be circular and cannot be completely detached from the rectangle. A valid stationary point may not be found due to certain constraints placed on a situation (greatest and least values). By examining the volume including all of the constraints, find which way to cut out the net of the tank to find the maximum volume. State any assumptions required to generate the solution and give strengths and limitations of the model considering that the car is medium sized.
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