A lidless rectangular box is to be manufactured from a single 30 by 40 inch cardboard sheet. The manufacturer will cut squares of size h from all four corners, fold up the ends and sides, and join the edges with heavy tape (see the figure on the last page). The box manufacturer would like to choose h (and, indirectly, w and l) such that the volume of the resulting box is maximized.
a) Provide an algebraic formulation of the box manufacturer’s problem. Clearly state your decision variables, objective function, and constraints.
b) Implement your model in Excel and find at least a local optimum.