Tiêu đề Linear Programming Board CQ & MCQ Practice Sheet Solution.pdf ✅

†hvMvkÖqx †cÖvMÖvg  Board CQ & MCQ Practice Sheet Solution 1 Rhombus Publications 02 †hvMvkÖqx †cÖvMÖvg Linear Programming WRITTEN 1| F1 I F2 Lv‡` ̈i cÖwZ †KwR‡Z wfUvwgb C I D Gi cwigvY I Zv‡`i g~‡j ̈i GKwU QK: [Xv. †ev., w`. †ev,, h. †ev., wm. †ev. 18] Lv` ̈ wfvUvwgb C wfUvwgb D cÖwZ †KwRi g~j ̈ F1 6 2 3 F2 3 5 5 (K) †hvMvkÖqx †cÖvMÖvg Gi `yBwU myweav D‡jøL Ki| (L) •`wbK wfUvwgb C I D Gi b~ ̈bZg Pvwn`v h_vμ‡g 60 GKK 50 GKK n‡j, Kg Li‡P •`wbK wfUvwgb Pvwn`v †gUv‡bvi GKwU †hvMvkÖqx †cÖvMÖvg MVb Ki| (M) †jLwP‡Îi mvnv‡h ̈ 2(L)-G cÖvß †hvMvkÖqx †cÖvMÖvgwU mgvavb K‡i •`wbK me©wb¤œ LiP wbY©q Ki| mgvavb: (K) †hvMvkÖqx †cÖvMÖvg Gi `yBwU myweav wb‡¤œ D‡jøL Kiv n‡jv: (i) mxwgZ cwigvY g~jab, KuvPvgvj, Rbej I hš¿cvwZ `ÿZvi m‡1⁄2 h_vm¤¢e Kg e ̈envi K‡i Drcv`‡bi Kvw•ÿZ cwigvY I ̧YMZ gvb wbwðZKiY| (ii)AbvKvw•ÿZ cÖwZeÜKZv wPwýZ I `~ixKi‡Yi Øviv Drcv`b e ̈q Kgv‡bv Ges me©vwaK gybvdv AR©b| (L) g‡b Kwi, Kg Li‡P •`wbK wfUvwgb Pvwn`v †gUv‡bvi Rb ̈ x †KwR F1 Lv` ̈ Ges y †KwR F2 Lv` ̈ cÖ‡qvRb| Afxó dvskb: Z = 3x + 5y (me©wb¤œKiY) mxgve×Zv: 6x + 3y  60 (wfUvwgb C) 2x + 5y  50 (wfUvwgb D) Ges x  0, y  0 (Ans.) (M) ÔLÕ n‡Z cvB, Afxó dvskb: Z = 3x + 5y (me©wb¤œKiY) mxgve×Zv: 6x + 3y  60 2x + 5y  50 x  0, y  0 AmgZv ̧‡jvi Abyiƒc •iwLK mgxKiY: Avevi, 6x + 3y = 60 2x + y = 20  x 10 + y 20 = 1 ........... (i) 2x + 5y = 50  x 25 + y 10 = 1 ........... (ii) x = 0 ........... (iii) y = 0 ........... (iv) QK KvM‡R g~jwe›`y O Ges x I y Aÿ‡K h_vμ‡g XOX Ges YOY Øviv wPwýZ K‡i (i), (ii), (iii) I (iv) bs mgxKi‡Yi †jL A1⁄4b Kwi| (†hLv‡b, x Aÿ I y Aÿ eivei †QvU 1 e‡M©i evûi •`N© ̈ = 1 GKK)| Y X Y X B(0,20) A(10,0) O C(25,0) D(0,10) E( ) 25 4  15 2 CE Ges EB †iLvsk؇qi Dci ̄’ I Zv‡`i Wvbcvk¦© ̄’ we›`ymg~‡ni †mU cÖ`Ë mKj kZ©‡K wm× K‡i weavq H AÂjwUB mgvav‡bi AbyK‚j GjvKv|  cÖvwšÍK we›`y ̧wj C(25, 0), E     25 4  15 2 Ges B(0, 20) C(25, 0) we›`y‡Z Z = 3  25 + 5  0 = 75 E     25 4  15 2 we›`y‡Z Z = 3  25 4 + 5  15 2 = 56.25 B(0, 20) we›`y‡Z Z = 3  0 + 5  20 = 100  E     25 4  15 2 we›`y‡Z Z Gi gvb me©wb¤œ A_©vr Zmin = 56.25|  me©wb¤œ 56.25 UvKv LiP K‡i •`wbK wfUvwgb Pvwn`v †gUv‡bv m¤¢e| myZivs 25 4 †KwR F1 Lv` ̈ Ges 15 4 †KwR F1 Lv` ̈ Ges 15 2 †KwR F2 Lv` ̈ cÖ‡qvRb| (Ans.)