Title Liner Programming Engg Practice Sheet Solution [HSC 26].pdf ✅

2  Higher Math 2nd Paper Chapter-2 MCQ weMZ mv‡j KUET-G Avmv cÖkœvejx 1. GKRb e ̈emvwq 40 UvKv †KwR `‡i †cqviv Ges 120 UvKv †KwR `‡i Av‡cj wKb‡Z cv‡ib| Dfq cÖKvi wg‡j wZwb Zvi †`vKv‡b †gvU 120 †KwR dj ivL‡Z cv‡ib| D3 e ̈emvwq †cqviv wewμ K‡i cÖwZ †KwR‡Z 16 UvKv Ges Av‡cj wewμ K‡i cÖwZ †KwR‡Z 32 UvKv jvf Ki‡Z cv‡ib| hw` wZwb m‡e©v”P 12000 UvKv wewb‡qvM Ki‡Z cv‡ib, Zvn‡j †Kvb cÖKv‡ii dj KZ †KwR wb‡j wZwb m‡e©v”P jvf Ki‡Z cvi‡eb? [KUET 16-17] 120 †KwR †cqviv 120 †KwR Av‡cj 30 †KwR Av‡cj I 90 †KwR †cqviv 90 †KwR Av‡cj I 30 †KwR †cqviv 60 †KwR Av‡cj I 60 †KwR †cqviv DËi: 90 †KwR Av‡cj I 30 †KwR †cqviv e ̈vL ̈v: x, y ≥ 0 x + y = 120 ...... (i) 40x + 120y ≤ 12000 ...... (ii) Z = 16x + 32y Y X X Y O(0, 0) D(120, 0)(300, 0) C(30, 90) (0, 120) (0, 100) †KŠwYK we›`ymg~n (30, 90), (120, 0), (0, 100) m‡e©v”P jvf, Zmax = 16  30 + 32  90 = 3360 2. A I B cÖKvi †Ljbv •Zwi‡Z h_vμ‡g 5 I 3 GKK kÖg Ges 3 I 4 GKK KuvPvgvj jv‡M| A cÖKv‡ii cÖwZwU †_‡K 10 UvKv I B cÖKv‡ii cÖwZwU †_‡K 12 UvKv jvf Kiv m¤¢e nq Ges †Kv¤úvwbwU 165 GKK kÖg I 132 GKK KuvPvgvj †hvMvb w`‡Z cv‡i, Z‡e m‡e©v”P †h jvf n‡e Zv n‡jvÑ [KUET 14-15] 330 taka 360 taka 420 taka 448 taka 650 taka DËi: 420 taka e ̈vL ̈v: awi, h_vμ‡g x I y GKK A I B †Ljbv •Zwi Ki‡Z n‡e| 5x + 3y ≤ 165 ; 3x + 4y ≤ 132 ; x, y  0 (24, 15) (33, 0) (44, 0) (0, 0) (0, 33) (0, 55) Y X †KŠwYK we›`ymg~n (0, 0), (33, 0), (24, 15), (0, 33)  m‡e©v”P jvf, Zmax = 10x + 12y = 10  24 + 12  15 = 420 taka 3. A I B cÖKvi hš¿ •Zwi‡Z h_vμ‡g 15 I 5 GKK mgq Ges 5 I 10 GKK KuvPvgvj jv‡M| 105 GKK mgq I 60 GKK KvuPvgvj w`‡q m‡e©v”P †h jvf n‡e (hLb A Gi cÖwZ GK‡K jvf 50 UvKv Ges Zv B Gi Rb ̈ 30 UvKv), Zv n‡jvÑ [KUET 13-14, 12-13] 390 UvKv 420 UvKv 380 UvKv 400 UvKv 350 UvKv DËi: 390 UvKv e ̈vL ̈v: awi, x GKK A I y GKK B •Zwi Ki‡ev|  15x + 5y ≤ 105; 5x + 10y ≤ 60; Z = 50x + 30y (6, 3) (7, 0) (12, 0) (0, 0) (0, 6) (0, 21) Y X †KŠwYK we›`ymg~n, (0, 0), (0, 6), (7, 0), (6, 3)  m‡e©v”P jvf, Zmax = 50  6 + 30  3 = 390 weMZ mv‡j IUT-G Avmv cÖkœvejx 4. Alal and Dulal shopped at the same store. Alal bought 5 kg of apples and 2 kg of bananas and paid altogether BDT 22. Dulal bought 4 kg of apples and 6 kg of bananas and paid together BDT 33. Find the cost 1 kg bananas. [IUT 18-19] BDT 3.5 BDT 3 BDT 2.5 BDT 4.5 DËi: BDT 3.5 e ̈vL ̈v: cost of 1 apple = x; cost of 1 banana = y As per Overstion 5x + 2y = 22; 4x + 6y = 33 Solving, x = 3; y = 3.5 5. A company produces 2 types of product. It uses 3 plants for the production. The 1st product requires one hour in plant 1 and 3 hours in plant 3 for producing 1 item. The 2nd product requires 2 hours each in plant 2 and for one production. Total available hours in plants 1, 2 in a week are 4, 12 and 18 respectively. Profit for each item of product 1 is 3 thousand, and for product 2 is 5 thousand. The possible maximum weekly profit for the company is- [IUT 16-17] 18 thousand 33 thousand 36 thousand 3 thousand DËi: 36 thousand