3. (20 points) A home building store faces the following problem. Their customers demand plywood in the sizes of 4x3 meters, 4x5 meters and 4x6 meters. Customer demand for these three sizes is estimated to be at least 20, 50 and 40, and customers are prepared to pay £ 7, £ 9 and £ 10 for each of these sheets, respectively. The store must generate these sizes by cutting up standard 4x8 meter sheets, each of which costs them £ 6. These sheets are in unlimited supply. Furthermore, each cut costs the store $ 1.50. Maximizing profit, develop a linear integer model for finding an optimal cutting plan of 4x8 meter sheets. Clearly define your decision variables.