Linear Programming [Optionals IAS Mains Mathematics]: Questions 1 - 5 of 20

• Given with constrains , ,
• For graph, we convert the inequalities into equation.

  and

• In equation

  If

• Then

  Point is

  If

• Then

  point is

• In equation

• If then

  Point is

• If then

  Point is

• Plotting these equations on the graph. Area of in the figure satisfied by the constraint is shown by the shaded area and is called…

• After introducing slack variable in the constraint, we convert inequalities into equalities, and assign coefficient to slack variable in the objective function. The resultant objective function and constraint equation are given below.

  Subject to

• The table for simplex computation are shown below.
• Since all the elements of Cj-Zj row are or zero, so w…

Given,

Subject to The given system of Equation can be written in the matrix from as where

Since, Rank of A is 2

Then Maximum No. of linearly independent columns of A is 2. Thus we can take any of the following sub-matrices as basis matrix B.

Let us take first . A basic solution to the given system is now obtained by setting and solving the system.

…

Using Hungarian method by Kuhn

Step (1) : Row Reduction

Subtracting the mimimum element of each row from all the element of that row.

Table 1

Step (2) : Column Reduction

Table 2

Step (3) : Making Assignments

Table 3

The No. of assignment are less than 5 so, we draw minimum number if lines to …

By using VAM- Initial feasible solution we get

Noted that there are allocations which are necessary to forced further.

The minimum transportation cost is