Maximize Opening in Prison Gate

Question

A prisoner is plotting an escape. The prison gate is made of n horizontal bars and m vertical bars, spaced exactly one unit apart, so they form a grid in which every opening starts out as a 1 x 1 square. The grid sits inside a fixed outer frame, one unit beyond the first and last bar in each direction, and the frame cannot be removed. By taking out some of the bars, the prisoner can merge openings into bigger ones. ...