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?
This problem is an assignment problem, which can be solved using the Hungarian algorithm to minimize the total man-hours. The given cost matrix is: \[ \begin{array}{c|ccccc} ______ _________ _________ _________ _____ _________.
________ ____ ____ ___ _____ _________ ______ ____ __________ _____ ________.
__________ __________ _________ _________ _____ ______ _________ ____ __________ ___ _____ ___.
___ ____ _____ ______ ___ __________ ____ ___ _________ __________ ___.
__________ _______ ___ ________ ______ ________ _________ _____ ______ __________ __________.
_______ _______ ________ ________ ___ _____ _______ ____ ______ ______.
___ _________ __________ ______ ____ _____ _________ __________ ______ ___ _______.
________ __________ _______ ____ _______ ________ ____ ______ _________.
_________ _____ ________ __________ ________ ____ ______.
____ ________ __________ ___ ____ __________ _______ ___ _________ ___ __________.
_________ ________ _____ ____ ________ ________ ______ ________.
_____ __________ _______ _________ ___ ____ _____.
___ _______ ________ _________ ________ ________ ____.
_______ __________ _______ ________ ______ ___ ______ _________ _________.
__________ _________ ________ ___ _____.
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k के किस मान के लिए निम्नलिखित सदिश, रैखिकतः स्वतंत्र हैं?
Write the LPP formulation of the following assignment problem:
निम्नलिखित आद्य रैखिक प्रोग्रामन (LP) समस्या की द्वैती प्राप्त कीजिए :
z = x1 - 2x2 + 3x3 का अधिकतमीकरण कीजिए
जबकि -2x1 + x2 + 3x3 = 2
2x + 3x2 + 4x3 =1
X1,X2X2 ≥ 0
निम्नलिखित रैखिक प्रोग्रामिंग (एलपी) समस्या को एकल विधि का उपयोग करके हल करें:
z = 6x1 + 4x2 का अधिकतमीकरण कीजिए
जबकि 2x1 + 3x2 ≤ 30
3x1 + 2x2 ≤ 24
x1 + x2 ≥ 3
x1 , x2 ≥ 0
उत्तर-पश्चिम कोना विधि का प्रयोग करके निम्नलिखित परिवहन समस्या का प्रारम्भिक आधारी सुसंगत हल ज्ञात कीजिए :
| 90 | 90 | 100 | 110 | 200 |
| 50 | 70 | 130 | 85 | 50 |
| 75 | 100 | 100 | 30 |
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 2× 2 matrix game is 4, then p ≥ 4 .
c) If 10 is added to each of the entries of the cost matrix of a 3× 3 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 cj − zj ≥ .0
e) The dummy source or destination in a transportation problem is added to prevent solution from becoming degenerate.
Find all values of k for which the vectors:
are linearly independent.