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

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Question 1

Appeared in Year: 2016

Describe in Detail

Essay▾

Find the maximum value of with constrains , , by graphical method. [CS (Main) Paper 2]

Explanation

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

… (56 more words) …

Question 2

Appeared in Year: 2016

Describe in Detail

Essay▾

Maximize subject to is the optional solution unique justify your answer. [CS (Main) Paper 2]

Explanation

  • 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…

… (51 more words) …

Question 3

Appeared in Year: 2015

Describe in Detail

Essay▾

Consider the following liner programing problem:

Subject to

(i) Using the definition, find it՚s all basic solutions. Which of these are degenerate basic feasible solutions and which are non-degenerate basic feasible solution (s) is/are optimal?

(ii) Without solving the problem, show that it has optimal solution. Which of the basic feasible solution/ (s) is/are optimal? (CS main Paper 2)

Explanation

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.

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Question 4

Appeared in Year: 2015

Describe in Detail

Essay▾

Solve the following Assignment problem to minimize the Sales

Assignment Problem to Minimize the Sales

(CS Paper 2)

Explanation

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

Row Reduction in Image

Step (2) : Column Reduction

Table 2

Column Reduction in Image

Step (3) : Making Assignments

Table 3

Making Assignments

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

… (177 more words) …

Question 5

Appeared in Year: 2014

Describe in Detail

Essay▾

Find the initial basic feasible solution to the following transportation problem by Vogel՚s approximation method. Also, find its optimal solution and the minimum transportation cost:

Destination and Origins Are Given in Table
Destinations
OriginsSupply
1514
2716
625
Demand154-

(CS paper -2)

Explanation

By using VAM- Initial feasible solution we get

VAM- Initial Feasible Solution

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

The minimum transportation cost is