An open-top box is to be made by cutting congruent squares from the corners of a 15cm x 15 cm sheet of metal by bending up the sides a) what equation relates the side length z of the removed squares and the volume v of the box?
b) determine the region of feasibility for x. show all algebra for the solution
c) compute a formula for dV/dx
d) find all critical points for the curve V. show all algebra for the solution
e) find the maximum volume a box constructed in this way can have, as well as the dimensions that achieve that volume. show all substitutions for the solution. do not approximate your value