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3. Goti and Monu are playing a game. Goti is starting a play. Goti & Monu have 3 strategies each. Decide the outcome of the game. 5 1 6 G3 8 3 2 G2 7 5 8 G1 M3 M2 M1

5. Solution . . 8 5 8 COLUMN MAXIMA 1 5 1 6 G3 2 8 3 2 G2 5 7 5 8 G1 ROW MINIMA M3 M2 M1

7. Ajay International furnishings makes only 2 products – tables & chairs. He gets a profit of 4$ on table and $3 on chair. He has only 2 machines (M1 &M2) with constraints of max. 30 hours and 24 hours of working per week. Suggest how much should he make and of which type? (Table requires 2 hour of M1 and 1 hour of M2. Chair requires 1 hour of M1 and 2 hour of M2)

10. Initial solution – no production 3 4 C- Z o 0 Profit Z 1 0 2 1 24 0 S2 0 1 1 2 30 0 S1 S2 S1 C T Qty 0 0 3 4 Profit C

12. C- Z Profit Z S2 S1 0 0 Profit C 24 30 Qty 4 0 1 2 T 4 3 o 2 1 C 3 0 1 S1 0 1 0 S2 0 24 15 Row sel.

13. Second Table C- Z Profit Z S2 T 0 4 Profit C 9 15 Qty 0 4 0 1 T 4 1 2 1.5 .5 C 3 -2 2 -.5 .5 S1 0 0 0 1 0 S2 0 6 30 Row sel.

14. Final Solution C- Z Profit Z C T 3 4 Profit C 66 6 12 Qty 0 4 0 1 T 4 0 3 1 0 C 3 -1.6 1.6 -.33 .66 S1 0 -.66 .66 .66 -.33 S2 0 30 Row sel.

15. Table No. 2 Calculation of 2 nd row. . . 0 –(.5*.66)=-.33 .66 .5 0 .5-(.5*-.33)= .66 -.33 .5 .5 .5-(.5*1)=0 1 .5 .5 1-(.5*0)=1 0 .5 1 15- (.5*6)=12 6 .5 15 Old – (KC*NR) New Row Key Column Old value

16. Table No. 1Calculation of 2 nd row 1 0 1 1 -.5 .5 1 0 2 1 24 Old value 1 1 1 Key Column .5 1 15 New Row 1.5 1-(1*1) = 0 24-(1*15) =9 Old – (KC*NR)

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