Simplex Method
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; Choeter ''f . L ?f * slMpLEX r4ETHoD A firm rnanufactures two products A & B on which tbe p"rofi* earned per unit are Rs. 3 and Ash Profits in,, (%r) rapees per ton 2.0 t 2.00 3.0 t 5.00 5.0 t 4.00 Rs. 4 respectively. Each product is pracessed.on two. mac.Ejltei"M1 and M2. Product A requires one minute of processing time on M 1 and two minutes o.n M2, while B requires one minute on M 1 and one minute on M2. Machine M 1 $ avai!_able f9r ,01 -o!g than 7 hrs. 30 m\s. while machine M 2 is available for I 0 hrs. during any working day Find the number of units df products A and B to be manufactured to get maximu.m-p761iy. ' ..'; ;.' ''' ' t,l:l sri i#ltip.tefi itub, th Ad Ay'sdh e' 7ft;6; foltowirt !, pro bl em : 1-. ; |,i ni4'i,MwtW.gi $ *.Zxi +..,'5X,$, ''j,;, :' . i '. . .}.'i,su6ieetb'"J6it,+"4h€.&)l,.i..;..J.'." .'r ,: J"{i;i ,:l :,: ii, : l; :r4;r,.' $fi7.l +'ggp.rgi',?l; Xt, x2 2 A. i maximizeZ = 4x1 *3x2*6yr, subject to 2x1 * 3x2 * 2xs < 440, 4xt +3xr <470, 2x1*Jq <430, Xl, X2, -f3 2 0. Three grades of cool A, B and C contain'phosphorus'and'ash- ai'impurities. fn o pdrtictilar rlal Prgcess, frel up to 100 ton (maximum) is required which shouid contain,ash not more than 394 and phosphorus not more than 0.03%. It is deiired to maximtrze the profi, *iit",riiOis l-hese conditions. lhere is an unlimited supply of each grade. The percentage of impurities and the profits of grades are given below. Coal Phosphorus A B C (%") 0.02 0.04 0.03 Find the proportions in which the three grades be used. by simplex method the foltowing L.p. problem . Minimize Z : xt - 3xz + 3xt, subject to ixr - xz * 2xt 2x, + 47, 4x1*3x2*$7t X1, X2, Xj 2 0. / Food X contains 6 units of vitamin A per gram and 7 units of vitamin B per gram ancl costs l2 paise'per gram. Food Y contains I units of vitamin A per grom and l2 unit, oJuttamin B per gram and costs 20 paise per gram. The daily minimum requirement of vitamin A ancl vitamin B is 100 units and 120 units respectively. Find the minimum cost of p:roduct mix by the simplex method. MaximizeZ:3x1-x2, subject to 2x, + x2 S 2, xr*3x223, x254, X1, X2 2 0. <7 > - 12, n f.;.dat b3 <''-''rxe[;-3 bfl] S 10, */2<-1 kxz 1 ,Z 4. 3. 5. 6. 1,
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Linear Programming problem
Transcript of Simplex Method
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; Choeter ''f . L ?f * slMpLEX r4ETHoDA firm rnanufactures two products A & B on which tbe p"rofi* earned per unit are Rs. 3 and
Ash Profits in,,(%r) rapees per ton2.0 t 2.003.0 t 5.005.0 t 4.00
Rs. 4 respectively. Each product is pracessed.on two. mac.Ejltei"M1 and M2. Product A requiresone minute of processing time on M 1 and two minutes o.n M2, while B requires one minute on M 1and one minute on M2. Machine M 1 $ avai!_able f9r ,01
-o!g than 7 hrs. 30 m\s. while machineM 2 is available for I 0 hrs. during any working day Find the number of units df products A andB to be manufactured to get maximu.m-p761iy. ' ..'; ;.' ''' '
t,l:l sri i#ltip.tefi itub, th Ad Ay'sdh e' 7ft;6; foltowirt !, pro bl em :1-. ; |,i ni4'i,MwtW.gi $ *.Zxi +..,'5X,$, ''j,;, :' . i '. ..}.'i,su6ieetb'"J6it,+"4h.&)l,.i..;..J.'."
.'r ,: J"{i;i ,:l :,: ii, : l; :r4;r,.' $fi7.l +'ggp.rgi',?l;
Xt, x2 2 A. i
maximizeZ = 4x1 *3x2*6yr,subject to 2x1 * 3x2 * 2xs < 440,
4xt +3xr
