Solve the following LPP graphically:
Maximize:
$
subject to the constraints:$
$
$
b) Find all values of k for which the vectors:$
are linearly independent.
The constraints are first plotted in the first quadrant. The line (4x_1+3x_2=12) cuts the axes at ((3,0)) and ((0,4)). The line (6x_1+18x_2=36), or equivalently (x_1+3x_2=6), cuts the axes at ((6,0)) and ((0,2)). With (x_1,x_2\ge0), the feasible region is the common area below __________ __________ ___ _________ ________.
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Reduce the following two person zero sum game to game using principle of dominance. And hence solve the game.
Player B
b) Obtain the dual of the following primal LP problem:
Maximize
Subject to $
$
) निम्नलिखित दो खिलाड़ी शून्य योग खेल को प्रमुखता सिद्धांत द्वारा खेल में समानीत कीजिए और इस प्रकार खेल को हल कीजिए।
) Using matrix – minima method, find the initial basic feasible solution of the following transportation problem:
Hence find the optimal solution.
b) Check whether the following set is convex:
$
Solve the following LPP graphically:
Maximize:
$
subject to the constraints:$
$
$
b) Find all values of k for which the vectors:$
are linearly independent.
) For what value of k are the following vectors linearly independent?$
b) Solve the following LP problem using simplex method:
Maximize
Subject to $
$
$
. State which of the following statements are true and which are false. Give reasons for your answer with a short proof or a counter example.
a) The intersection of finite number of convex sets is not convex.
b) If value of the matrix game
is 4, then
.
c) If 10 is added to each of the entries of the cost matrix of a assignment problem, then the total cost of an optimal assignment for the changed cost matrix will increase by 10.
d) For maximization LP model, the simplex method is terminated when all values .
e) The dummy source or destination in a transportation problem is added to prevent solution from becoming degenerate.
Write the LPP formulation of the following transportation problem:
| Destination | Supply | |||
|---|---|---|---|---|
| $D_1$ | $D_2$ | $D_3$ | ||
| Source $O_1$ | 10 | 18 | 12 | 200 |
| Source $O_2$ | 15 | 17 | 9 | 300 |
| Source $O_3$ | 13 | 15 | 7 | 500 |
| Requirement | 400 | 200 | 400 |
