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Posted Date: 29 Aug 2007 Posted By:: kewal singh paneser Member Level: Gold Points: 5 (Rs. 1)
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2005 Punjab Technical University General M.Tech Machine Design Optimization Techniques Question paper
OPTIMIZATION TECHNIQUES MCE 505 M.TECH 3rd Sem. MAY 2005
I Use revised Simplex Method to solve the following:
Maximize z= 6x1 + 3x2 + 4x3 – 2x4 + x5
Subject to 2x1 + 3x2 + 3x3 + x4= 10
x1 + 2x2 + x3 + x5= 8
x1 , x2 , x3 , x4, x5 =0
II By dynamic programming technique, solve the problem:
Minimize z= x12 + x22 + x32
Subject to constraints x1 + x2 + x3 =15
and x1 , x2 , x3 =0
III (a) Discuss application of Quadratic Programming
(b) Solve the following quadratic programming problem:
Minimize f(x1,x2) = - 4 x1 +x22 – 2 x1x2 +2x22
Subject to constraints 2x1 +x2 = 6
X1- 4x2 = 0
X1, x2 =0
IV A tax consulting firm has our service stations (counters) in its office to receive people who have problems and complaints about their income, wealth and sales taxes. Arrivals average 80ersons in an 8 hour ser vice day. Each tax Adviser spends an irregular amount of time servicing the arrivals which have been found to have an exponential distribution. The average service time is 20 minutes. Calculate the following:
(a) the average number of customers in the queue.
(b) The average number of customers waiting to be serviced in the system.
(c) The average time a customer spends in the system.
(d) The average waiting time for a customer.
V Use two-phase simplex method to minimize:
Z = x1 +x2 +x3
Subject to constraints x1 -3x2 +4x3 =5
x1 -2x2 = 3
2x1 -x2 = 4 and x1 ,x2 = 0 but x3 is unrestricted
VI (a) What is heuristic programming? What is the need of it? Explain using traveling salesman problem.
(b) Explain with the help of an example the difference between constrained and unconstrained optimization.
VII (a) Solve he following non-linear programming problem, using the method of Langrangian multipliers.
Minimize Z = x12 +x22+x32
Subject to the constraints x1 +x2 +3x3 = 2
5x1 +x2 +2x3 = 5
(b) Discuss Classical Method of Optimization
VIII Write short notes on the following:
(a) Applications of dynamic programming.
(b) Sensitivity analysis
(c) Assembly line balancing
(d) Dynamic Programming vs. Linear Programming.
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