Quantitative Methods Problem Sets: Linear Programming Model and Graphical Solution to Linear Programming Problems Linear Programming Model. Build the LP Model that represents each problem. 1. LP Model: A manufacturer wishes to produce commodities, X and Y. The number of material, labor, and equipment needed to produce one unit of each commodity is shown below together with the available number of units of each item. Available X Y units Material 6 480 Labor 2 240 Equipment 0 200 Profit/ unit P120 P100 Build the LP Model for the problem to determine the number of units to produce in order to maximize the profit (P)