solve and explain LP graphical solution method max z=3x1+5x2 x1/800+x2/700 =0 soruyu bu ekilde cevap yazarmsnz The given LP is a maximization problem with two

solve and explain LP graphical solution method max z=3x1+5x2 x1/800+x2/700<=1 x1/1500+x2/1200<=1 x1>=0 x2>=0 soruyu bu ekilde cevap yazarmsnz

The given LP is a maximization problem with two decision variables (x1 and x2) and two constraints. We can start by plotting the feasible region, which is the set of all points that satisfy both constraints. To do this, we can rewrite each constraint in slope-intercept form:

x2 -800/700 x1 + 700/700 x2 -1500/1200 x1 + 1200/1200

Then we can plot the two lines and shade the region that satisfies both constraints:

LP Graphical Solution

The feasible region is the shaded triangle in the graph above. We can see that it is bounded by the x-axis and the two constraint lines.

Next, we need to find the optimal solution that maximizes the objective function z=3x1+5x2 within the feasible region. To do this, we can use the corner-point method, which involves evaluating the objective function at each corner of the feasible region and choosing the corner that gives the maximum value of z.

The corners of the feasible region are the intersection points of the constraint lines. Solving the system of equations:

x2 = -800/700 x1 + 700/700 x2 = -1500/1200 x1 + 1200/1200

We get two corner points:

Corner 1: (0,0) Corner 2: (240,60)

We can then evaluate the objective function at each corner point:

Corner 1: z=3(0)+5(0)=0 Corner 2: z=3(240)+5(60)=840

Thus, the optimal solution that maximizes the objective function within the feasible region is at corner point (240,60), with a maximum value of z=840.

In summary, the LP graphical solution method involves plotting the feasible region and finding the optimal solution by evaluating the objective function at each corner of the feasible region. For this LP, the feasible region is a shaded triangle bounded by the x-axis and two constraint lines, and the optimal solution is at corner point (240,60), with a maximum value of z=840.