Thapar University 2006 M.C.A Opeartions Research - Question Paper

Thapar Institute of Engineering & Technology
MCA (1st Year)
Final Term exam
CA012(Opeartions Research)

Thapar Institute of Engineering & Technology, Patiala End Semester Examination Operations Research (CA-012)

vfc Time: 0900hrs. Duration: 3 hr$. Date: 08/12/2006 Max. Marks: 36

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Note: Attempt any six questions. Non-Programmable Scientific Calculators are allowed.

1. A company is producing a product which requires three parts at the final assembly stage. These three parts can be produced by two different departments as detailed below.

Production rate (units/hr)

Parti Part 2 Part 3 Cost(/hr)

Department 1    7    6    9    25.0

Department 2    6    11 5    12.5

In one week, 1050 finished (assembled) products are needed (but up to 1200 can be produced if necessary). If department 1 has 100 working hours available, but department 2 has 110 working hours available, FORMULATE the problem for minimizing the cost of producing the finished (assembled) products needed in one week as an LPP, subject to the constraint that limited storage space means that a total of only 200 unassembled parts (of all types) can be stored at the end of the week.    (6)

Solve following problem by 2 Phase Method

Max Z = -2x, - 4x₂ - x₃

s. t. x, + 2x₂ - x_i < 5 2x_l - x₂ +2x_} =2

- Xj + 2x₂ + 2x₃ 1

x,,x₂,x₃0

Solve following problem by Revised Simplex Method Max Z = 5x, - 4x₂ + 3x₃

s. t. 2x_x + x₂ - 6x₃ = 20

6x, + 5x₂ +10x₃ < 76

8x, - 3x₂ + 6x₃ > 22

Xj,X₂,X3 >0

4. For (M/M/c):(GD/oo/oo) model, Given that X = 15,/i = 5 and c = 4

Calculate P_s, P₀, Ls, Lq, Ws and Wq.    (6)

5(i) Find maximum flow from r to s for following graph (name the vertices yourself as 1,2,3... or a,b,c...)

7

(6)

P.T.O.

(ii) Find shortest paths from Node A* to all other nodes. A

(4+2)

(ii) Find Minimal Spanning Tree for following Graph

a I { fc
J 2	J4 vj

(4.5+1.5)

Solve the following problem by Generalized Simplex Method:

Min Z = 5*, +6x₂ -3x₃ s. t. 5x, + 5x₂ + 3x₃ 50 + x₂ - *3 20

lx_x + 6x₂ - 9jc₃ 30

x_ltx_2tx₃Z0    (6)

(a)    Solve the following constrained Non-Linear Programming Problem

Min Z = 3x,² + lx₂² + 5x* ^s*Si (0 = 2x, + 3x₂ + X3 - 5 = 0 g₂ (X) = 3x, + 5x₂ + 7x₃ - 2 = 0

(b)    Write generalized KKT conditions for generalized Non-Linear problems of Maximization nature.    (5+1)

Attachment: thapar-university-2006-m-c-a--26300-1.pdf

Earning:   Approval pending.