A department has five employees with five jobs to be performed. The time (in hours) each employee will take to perform each job is given in the following matrix. How should the jobs be allocated, one per employee, so as to minimize the total man hours?
b) For the following pay-off matrix, transform the zero-sum game into an equivalent linear programming problem:
### (a) Assignment Problem (Minimize Total Man-Hours) Jobs (A,B,C,D,E) must be assigned one-to-one to Employees (I,II,III,IV,V). Time matrix (hours): | Job \ Emp | I | II | III | IV | V | | --------- | -- | -- | --- | -- | -- | | A | 10 | 5 | 13 | 15 | 16 | | B | 3 | 9 | 18 | 13 | 6 | | C | 10 | 7 | 2 | 2 | 2 | | D | 7 | 11 | 9 | 7 | 12 | | E | 7 __________ ______ __________ ____ _____ ____ __________ __________ _____ ______.
___ __________ _____ ___ ___ _____ _________.
______ ____ ____ ________ ______ ________ ________ ________ ____ ____ ____.
_____ _____ _______ _____ _____.
_________ _________ ______ ___ ____ _________.
_____ _________ _____ ____ ___ ________ ________ ________ ________ _________ ______ _______.
________ ____ ____ __________ __________ __________ ___ _________ __________ _______ ___.
______ _____ _____ ____ _______ _____ _______ ____ ______ ________ ____.
___ _______ ____ __________ __________ ___ __________ ________ __________ _____ ________.
______ ___ ______ ______ ________ _______ ________ ____ ________.
________ _______ _______ ___ ________ __________ ___ ____.
______ _________ ______ ________ __________ ________ __________ __________ __________ __________ _____.
________ ________ ____ _____ ___.
____ ____ _____ _______ ____ _______ _____ _________ ______.
______ _____ __________ _____ _____ ___ _________ ________ ____.
_________ ________ _________ _________ _______ ____ ____ ____ ____ _____.
____ ____ _________ _________ _______ ________ ____ ___.
_________ ____ _________ ___ _______ _________ _______ ___ ___ ____.
________ ____ ______ ________ ____ ______ ____ ________ ________ ____ _________.
_____ __________ ___ _______ _____ ________.
_______ ________ __________ __________ ____ _______ __________ ________.
_________ _______ ___ ____ ______ ________ _____ ______ _______.
_____ _____ _________ _________ _________ _________ __________.
_______ _______ ___ ______ ______ _________ ___ _____ ____ ______ _______.
____ _______ _______ ________ _____ _________ _____ _____ __________ ______ ________.
___ _____ ________ _________ ______.
___ __________ ________ ______ ______ _______ _________ __________ ____ _____.
_______ _________ ___ ____ ____ ____ ___ ________ __________ ____ _________ ___.
_______ ________ ______ _________ __________ _______ ____.
___ _______ _____ ________ _________.
_________ _______ _________ ____ ________ _____ ______ __________ ___ _________ __________ ________.
_______ _____ ___ ____ __________ ___ __________.
________ ____ ___ _____ _____ ___.
________ _________ ________ _______ _____ _________.
____ __________ _____ ___ _________ ________ ____.
_____ _________ _________ _____ ____ _____.
Get Full Answer on WhatsApp
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 |
Solve the following LPP graphically:
Maximize:
$
subject to the constraints:$
$
$
b) Find all values of k for which the vectors:$
are linearly independent.
) 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:
$
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 $
$
A department has five employees with five jobs to be performed. The time (in hours) each employee will take to perform each job is given in the following matrix. How should the jobs be allocated, one per employee, so as to minimize the total man hours?
b) For the following pay-off matrix, transform the zero-sum game into an equivalent linear programming problem:
) निम्नलिखित दो खिलाड़ी शून्य योग खेल को प्रमुखता सिद्धांत द्वारा खेल में समानीत कीजिए और इस प्रकार खेल को हल कीजिए।
निम्नलिखित आद्य रैखिक प्रोग्रामन (एलपी) समस्या की द्वैती प्राप्त कीजिए :
का अधिकतमीकरण कीजिए
जबकि