Analysis of the available information and verification of the hypothesis using pre-established measure of effectiveness.
Action Phase –
The phase involves making recommendations for the decision process. The recommendation can be made by those who identify and present the problem or by anyone who influences the operation in which the problem has occurred.
Q. 2 a. Explain the graphical method of solving Linear Programming Problem.
b. A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper in a week. There are 160 production hours in a week. It requires 0.20 and 0.40 hours to produce a ton of grade X and Y papers. The mill earns a profit of Rs. 200 and Rs. 500 per ton of grade X and Y paper respectively. Formulate this as a Linear Programming Problem. ?
Ans Linear Program Problem - is a mathematical technique design to help managers in their planning and decision –making .It is usually used in an organisation that is trying to make the most effective use of its resources . Resoucrces typically include machinery , manpower , money, time , warehouse space and raw materials .
For obtaining an optimal solution to an LPP by graphical method, the statement of following theorems of linear programming is used:
The collection of all feasible solution to an LPP constitutes a coves set whose extreme points corresponds to the basic feasible solution.
There are finite number of basic feasible regions within the feasible solution space.
If the cnvex set of the feasible solution of the system of simultaneous equation is a covex polyhedron, than atleast one of the extreme points gives an optimal solution.
If the optimal solution occurs at more than one extreme point, the value of objective function will be the same for all convex combination of these extreme points
Formulation: Maximize: 200x + 500y Subject to: x<= 400 y<= 300 2x + 4y <= 1600 Solution: x = 200 tons y = 300 tons Profit = 190000
Q.3 a. Explain how to solve the degeneracy in transportation problems.
b. Explain the procedure of MODI method of finding solution through optimality test ?
Ans - Degeneracy in transportation problem –
A basic solution to an m- origin , n destination transportation problem can have the most m+ n-1 positive basic variable (non-zero) , otherwise the basic solution degenerates . It follows that whenever the number of basic cells is less than m+n-1, the transportation problem is degenerate one .
Degeneracy develops in two ways –