Lpp graphical method pdf

Now we will check the value of the objective function at the corner points of the feasible region ABCDE. In order to find the maximum value of the objective function the constraints of the objective function are drawn and the region formed by the constraints is the feasible region. The feasible region is a point here, therefore the given LPP ha an optimal solution and it will occur at point 3, 0.

A company manufactures two products P and Q with unit profit of 4 and 5, respectively. The production requires manpower and two kinds of raw materials R1 and R2. The following table summarizes the requirement and availability of resources.

If x and y are respectively the numbers of products P and Q. Then, the objective function is. Representing all the lines and intersections graphically, the five corner points are A 0, 9 , B 2, 8 , C 8, 2 , D 9, 0 and O 0, 0. Start Learning. Answer Detailed Solution Below - Answer Detailed Solution Below Option 2 : 0, 2. Get Started for Free Download App. Answer Detailed Solution Below 0. Concept: The minimum value can be obtained by the following steps Step1: Plot the constraints graphically Step2: Obtain the feasible region the region which is common for all the constraints Step3: Checking for the minimum value at the corner points, the point where minimum value occurs is the optimum point.

Answer Detailed Solution Below Option 2 : one solution. Answer Detailed Solution Below Concept: Let x are the units of P and y are the unit of Q. Objective function Max. Finding the corner points coordinates of B. The no. Answer Detailed Solution Below Option 4 : 8.

The correct answer is option 4. Hint The smart way to answer as per the given options. Constraint-1 Constraint-3 Constraint-4 Constraint-5 and Constraint Answer Detailed Solution Below Option 2 : 12, 5. Concept: The optimum value of the objective function is determined by plotting the constraints graphically and obtaining a feasible region common to all the constraints and then the optimum value of objective function is determined by checking the values at the corner points of the feasible region.

Draw the graph using the given constraints. The feasible region is ABC since the problem is of minimization type we are moving towards the origin. The minimum value of Z occurs at B 3, We find the feasible region using the given conditions.

Therefore we have the lines. Since both the decision variables x 1 , x 2 are non-negative ,the solution lies in the first quadrant of the plane.

There is no common region feasible region satisfying all the given conditions. Hence the given LPP has no solution. Exercise A company produces two types of pens A and B. Pen A is of superior quality and pen B is of lower quality. Profits on pens A and B are Rs 5 and Rs 3 per pen respectively. Raw materials required for each pen A is twice as that of pen B.

The supply of raw material is sufficient only for pens per day. Pen A requires a special clip and only such clips are available per day. For pen B, only clips are available per day. Formulate this problem as a linear programming problem. A company produces two types of products say type A and B.

Profits on the two types of product are Rs. The data on resources required and availability of resources are given below. Formulate this problem as a linear programming problem to maximize the profit. A company manufactures two models of voltage stabilizers viz. The assembly and testing time required for the two models are 0. Manufacturing capacity hours at present is available per week. The market for the two models has been surveyed which suggests maximum weekly sale of units of ordinary and units of auto-cut.

Profit per unit for ordinary and auto-cut models has been estimated at Rs and Rs respectively. Formulate the linear programming problem. Solve the following linear programming problems by graphical method. Developed by Therithal info, Chennai. Toggle navigation BrainKart.