You are provided a $3$ by $4$ grid and a number of puzzle pieces.

Write an Integer Feasiblity Program $($i$.$e$.$ an IP with $0$ as the objective function$)$ to check if it is

possible to place these pieces on the grid so that each of the $34=12$ squares in the grid is covered

by exactly one puzzle piece. You are not allowed to rotate or flip the puzzle pieces. This is indeed

possible, as the figure below indicates. Write down a formulation that finds such an arrangement

and that is general enough that the same strategy should allow you to handle any $mn$ grid and

any set of arbitrary puzzle pieces.