university, bhopal assignment question paper - Madhya Pradesh ...

M P BHOJ (OPEN) UNIVERSITY, BHOPAL
ASSIGNMENT QUESTION PAPER
2009-10
CLASS : M.Sc. Final SUBJECT: Mathematics
Paper - III - Operation Research
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First Assignment Max Marks - 30
Q.1. A Company produces two kinds of leather belts A and B . A is of superior quality and B is of
lower quality. The respective profits are Rs. 10 and Rs. 5 per belt. The supply of raw material is
sufficient for making 850 belts per day. For belt A special type of buckle is required and 500 are
available per day. There are 700 buckles available for belt B per day. Belt A needs twice as much
time as that required for belt b. & company can produce 500 belts of all of them were of type A.
Formulate LPP & solve it graphically.
Q2. Solve following transportation problem & test the optimality by MODI method.
F1 F2 F3 F4 SUPPLY
W1 21 16 25 13 8
W2 17 18 14 23 10
W3 32 27 18 41 12
DEMAND 20 15 15 30 20
Q3. Use Branch & Bound technique to find an solution
Max. Z = x 1 + 4 x2
Sub. to 2x1 + 4x2 ≤ 7
5x1 + 3x2 ≤ 15, x1 , x2 ≥ 0.
Q4. Solve the following pay-off matrix , determine the optimal strategies and value of game
A = 5 1
3 4
Q5. Solve the following by Simplex method to
Minimize z = x1 – 3x2 + 2x3
Sub. to 3x1 – x2 + 3x3 ≤ 7
-2x1 + 4x2 ≤ 12 & x1, x2 ≥ 0
Second Assignment Max Marks – 30
P.T.O.