Does every feasible region has both a maximum and a minimum?
Does every feasible region has both a maximum and a minimum?
If the feasible region is bounded then the objective function has both a maximum and minimum value.
How do you calculate feasibility region?
The feasible region is the region of the graph containing all the points that satisfy all the inequalities in a system. To graph the feasible region, first graph every inequality in the system. Then find the area where all the graphs overlap. That’s the feasible region.
What is the maximum value of the objective function for the feasible region?
Instead of testing all of the infinite number of points in the feasible region, you only have to test the corner points. Whichever corner point yields the largest value for the objective function is the maximum and whichever corner point yields the smallest value for the objective function is the minimum.
What is Z in LPP?
12.1. 4 Decision Variables In the objective function Z = ax + by, x and y are called decision variables. 12.1. 5 Constraints The linear inequalities or restrictions on the variables of an LPP are called constraints. The conditions x ≥0, y ≥0 are called non-negative constraints.
What is feasible solution in DAA?
A feasible solution is a set of values for the decision variables that satisfies all of the constraints in an optimization problem. The set of all feasible solutions defines the feasible region of the problem.
What is feasible region in graphical method?
The feasible solution region on the graph is the one which is satisfied by all the constraints. It could be viewed as the intersection of the valid regions of each constraint line as well. Choosing any point in this area would result in a valid solution for our objective function.
What is the maximum value of Z in the feasible region?
▸ Objective =x has a minimum, reached at both corners, and between the two corners. Example 1. Maximize z =2 x + y subject to 3 x + y ≥6, x + y ≥4, x ≥0, and y ≥0. Since the feasible region is unbounded there may be no maximum value of z. For x ≥4, ( x ,0) is a feasible solution. At ( x ,0), z =2 x.
Is the feasible region of 3x + 5 y = 7 unbounded?
It can be seen that the feasible region is unbounded. The corner points of the feasible region are A (3, 0), B (1½, ½), and C (0, 2). The values of 2 at these corner points are as follows. For this, we draw the graph of the inequality, 3 x +5 y <7, and check whether the resulting half plane has points in common with the feasible region or not.
What is the feasible region of the system of constraints?
The feasible region determined by the system of constraints, x+3y≥3, x+y≥2, x,y≥0, is as follows. It can be seen that the feasible region is unbounded. The corner points of the feasible region are A(3, 0), B(1½, ½), and C(0, 2). The values of 2 at these corner points are as follows.
How do you find the minimum value of Z in LPP?
Determine the minimum value of Z =3 x +2 y (if any), if the feasible region for an LPP is shown in Fig.LP.1. The feasible region (R) is unbounded. Therefore minimum of Z may or may not exist. If it exists, it will be at the corner point (Fig.LP.1).
