Suggested answer:
The intersection of the half planes 2x + y 3 and x - y 0 is shown as shaded region in the figure. Feasible region is an unbounded convex region at A (0, 3), Z = 6 (0) + 3 = 3 At B (1, 1), Z = 6(1) + 1 = 7 Consider any point say (4, 5), the va..
The intersection of the half planes 2x + y 3 and x - y 0 is shown as shaded region in the figure. Feasible region is an unbounded convex region at A (0, 3), Z = 6 (0) + 3 = 3 At B (1, 1), Z = 6(1) + 1 = 7 Consider any point say (4, 5), the va..Some Exceptional Cases
We may come across LPP which may have no feasible (infeasible) solution or may have unbounded solution. We conclude the chapter by giving one example for each of these exceptional cas..
Step 1:
Find the feasible region of the LL..
Which of the following is the graph of a linear system of constraints..
Which of the following is the graph of a linear system of constraints? => the feasible region or the constraint region or the linear graph or the linear region..
Which of the following is the graph of a linear system of constraints..
Which of the following is the graph of a linear system of constraints? => The linear graph or The linear region or The feasible region or The constraint region..
Corner Point Method
The optimal solution to a LPP, if it exists, occurs at the corners of the feasible region. The method includes the following st..
Step 4:
To maximise Z draw a line parallel to ax + by = k and farthest from the origin. This line should contain at least one point of the feasible region. Find the coordinates of this point by solving the equations of the lines on which it lies. To minimise Z draw a line parallel to ..
Step 3:
Corresponding to each constant, we obtain a shaded region. The intersection of all these shaded regions is the feasible region or feasible solution of the LPP. Let us find the feasible solution for the problem of a decorative item dealer..
Corresponding to each constant, we obtain a shaded region. The intersection of all these shaded regions is the feasible region or feasible solution of the LPP. Let us find the feasible solution for the problem of a decorative item dealer..Solving LPP Graphical Method
Graphical Method of Solution of a Linear Programming Problem - So far we have learnt how to construct a mathematical model for a linear programming problem. If we can find the values of the decision variables x 1 , x 2 , x 3 , ..... x n , which can optimise (maximize or minimize) the objective func..
Example:
Find the optimal solution in the above problem of decorative item dealer whose objective function is Z = 50x + 18y. In the graph, the corners of the feasible region are O (0, 0), A (0, 80), B(20, 60), C(50, 0) At (0, 0) Z = 0 At (0, 80) Z = 50 (0) + 18(80) = Rs. 1440 At (20, 6..
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