A film company needs to cut 15 long rolls and 10 short rolls of film from stock pieces. Each stock piece can be cut in one of two patterns. The first produces 5 long and 2 short rolls; the second yields 3 long and 5 short. Once a stock piece is cut the rest is wasted. Neither pattern can be used more than 4 times because the jig used to cut it will become too inaccurate. The company wants to find the allowable combination of patterns that will minimize the number of stock pieces needed. Formulate the problem as an integer linear programming (ILP) model.