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Q7. A drip tray is to be fabricated from a thin rectangular steel plate, 36cm × 24cm, by cutting squares of side v cm from each cornet and folding up the edges which are then welded up along the corner joints. The fold lines are shown by the dotted lines in Fig Q7.

a. Determine, using differential calculus, the value of x which maximizes the capacity of the tray.(14)

b. Calculate the maximum capacity of the tray. (2)