Rectangular sheet | My Assignment Tutor

It is possible to model the construction of a water reservoir by starting with a rectangular sheet of steel that is x metres wide and 3x metres long. Now cut a smaller square that is t metres on a side out of each corner of the larger sheet and fold up and weld the sides of the steel sheet to make an open vessel without a lid. a. Show that the volume of water that can be held by this reservoir is given by b. Determine the value of t if the goal is to maximise V for any given value of x. c. Is there a value of x that maximises the volume of water that can be stored? d. Suppose that a civil engineer is constrained to use only 1 000 000 square metres of steel sheet to construct a water reservoir. This constraint can be represented by the equation  (because the builder can return the cut-out squares for credit). How does the solution to this constrained maximum problem compare with the solutions described in parts (b) and (c)?

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