3. Solve the following Linear Programming problem using graphs and interpret your results. A woodworker builds and sells band-saw boxes. He manufactures two types of boxes using a combination of three types of wood, maple, walnut and cherry. To construct the Type I box, the carpenter requires 2 board foot (bf) (The board foot is a specialized unit of measure for the volume of lumber. It is the volume of a one-foot length of a board one foot wide and one inch thick) maple and 1 bf walnut. To construct the Type Il box, he requires 3 bf of cherry and 1 bf of walnut. Given that he has 10 bf of maple, 5 bf of walnut and 11 bf of cherry and he can sell Type I of box for $120 and Type Il box for $160, how many of each box type should he make to maximize his revenue? Assume that the woodworker can build the boxes in any size, therefore fractional solutions are acceptable. The decision variables in this problem are the number of Type I and Il boxes to be built. They are denoted by x, and x, respectively. Since the goal is to maximize revenues and the revenues are a function of the number of boxes of each type sold, we can represent the objective function as max z = 120x, +160x2 One of the constraints in this problem is availability of different types of wood. Therefore, based on the number of boxes produced, the sum of the total wood requirement must be less than or equal to the available amount of wood for each type. We can represent this type of constraint with three inequalities referring to maple, cherry and walnut respectively as follows: Page 1 of 2 2x, 510 3x, s11 x + x, 55 In addition, there are the non-negativity constraints which ensure that our solution does not have negative number of boxes. These constraints are shown as *7, X, 20