EXAMPLE (Part 2): Graphical methodResolve using the Graphical Method the following problem:MaximizeZ = f(x,y) = 3x + 2ysubject to:2x + y ? 182x + 3y ? 423x + y ? 24x ? 0 , y ? 01. Initially we draw the coordinate system correlating to an axis the variable x, and the other axis to variable y, as can see in the figure.2. We mark, in these axis, a numerical scale appropriate to the values it can take the variables according to the constraints of the problem. To do this work, for each constraint we must to void all variables except the related to a certain axis, so we establishing the right value for such axis. This process must be done for every axis.3. Following, we represent all constraints. We take the first one and we draw the line that is obtained by considering the constraint as an equality. In the figure, this is represented with the A-B edge, and the region that defines this constraint is shown in YELLOW color. We repeat the process with the other restrictions, limiting BLUE and RED regions for the second and third constraint respectively.4. Feasible region is determined for the intersection of every region defined by the constraints and the non-negativity condition of each variable, that is, both axis. This feasible region is represented by the O-F-H-G-C polygon, in VIOLET color.5. Since there is a feasible region, we proceed to determine its extreme points, or vertices of the polygon that represents. These vertices are the candidate points for o ...
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