Assignment:
From a rectangular sheet of metal measuring 120mm by 75mm, equal squares of side x are cut from each of the four corners. The remaining flaps are then folded upwards to form an open box.
a) Draw a neat and simple diagram of the rectangular sheet of metal and show the dimensions (not drawn to scale) given including the squares of side x.
b) Show that the volume of the box is given by:
V= 9000x - 390x^2 + 4x^3
c) Find the value of x such that the volume is a maximum.
Provide complete and step by step solution for the question and show calculations and use formulas.