# LINEAR PROGRAMMING SOLUTION – GRAPHICAL METHOD

INTRODUCTION
There are two methods available to find an optimal solution to a Linear Programming Problem. One is a graphical method and the other is a simplex method. The graphical method can be used only for a two-variable problem i.e. a problem that involves two decision variables. The two axes of the graph (X & Y axis) represent the two decision variables X1 & X2

METHODOLOGY OF GRAPHICAL METHOD

EXERCISES

1. What is meant by feasible region in graphical method.
2. What is meant by ‘iso-profit’ and ‘iso-cost line’ in graphical solution.
3. Mr. A. P. Ravi wants to invest Rs. 1, 00, 000 in two companies ‘A’ and ‘B’ so as not to exceed Rs. 75, 000 in either of the company. The company ‘A’ assures average return of 10% in whereas the average return for company ‘B’ is 20%. The risk factor rating of company ‘A’ is
4 on 0 to 10 scale whereas the risk factor rating for ‘B’ is 9 on similar scale. As Mr. Ravi wants to maximise his returns, he will not accept an average rate of return below 12% risk or a risk factor above 6. Formulate this as LPP and solve it graphically.
4. Solve the following LPP graphically and interpret the result.
Max. Z = 8X1 + 16 X2
Subject to:
X1 + X2 ≤ 200
X2 ≤ 125
3X1 + 6X2 ≤ 900
X1, X2 ≥ 0
5. A furniture manufacturer makes two products – tables and chairs. Processing of these products is done on two types of machines A and B. A chair requires 2 hours on machine type A and 6 hours on machine type B. A table requires 5 hours on machine type A and no time on Machine type B. There are 16 hours/day available on machine type A and 30 hours/day on machine type B. Profits gained by the manufacturer from a chair and a table are Rs. 2 and Rs. 10 respectively. What should be the daily production of each of the two products? Use graphical method of LPP to find the solution