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 $
$
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. 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.
Solve the following LPP graphically:
Maximize:
$
subject to the constraints:$
$
$
b) Find all values of k for which the vectors:$
are linearly independent.
) निम्नलिखित दो खिलाड़ी शून्य योग खेल को प्रमुखता सिद्धांत द्वारा खेल में समानीत कीजिए और इस प्रकार खेल को हल कीजिए।
बताइए निम्नलिखित कथनों में से कौन-से कथन सत्य हैं और कौन-से असत्य। अपने उत्तर की पुष्टि एक संक्षिप्त उपपत्ति या प्रत्युदाहरण द्वारा कीजिए
a) परिमित संख्या में अवमुख समुच्चयों का सर्वनिष्ठ अवमुख नहीं होता है।
b) यदि आव्यूह खेल
का मान 4 हो, तो
।
c) यदि किसी नियतन समस्या में लागत आव्यूह की प्रत्येक प्रविष्टि में 10 जोड़ा जाए, तो परिवर्तित लागत आव्यूह के लिए इष्टतम नियतन की कुल लागत में 10 की वृद्धि हो जाएगी।
d) किसी अधिकतमीकरण रैखिक प्रोग्रामन (LP) निदर्श में, जब सभी मान हों, तो एकधा विधि सम्पन्न हो जाती है।
e) एक परिवहन समस्या में अपभ्रष्ट हल से बचने के लिए काल्पनिक (dummy) स्रोत या गंतव्य जोड़ा जाता है।
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:
) 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 $
$