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10锛庡柈绱斿舰娉曠殑瑷堢畻姝ラ鍙婂闅涢亱鐢�銆�
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3锛庡皪鍋跺柈绱斿舰绠楁硶鐨勮▓绠楁椹熷強瀵﹂殯鎳�(y墨ng)鐢�銆�
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閷垨鏈伕鑰咃紝瑭查涓嶅緱鍒�銆傛瘡灏忛 2 鍒�锛屽叡 20 鍒嗭級
1. 鍦ㄧ窔鎬ц(gu墨)鍔冩ā鍨嬩腑锛屾豢瓒崇磩鏉熸浠跺拰闈炶矤姊濅欢鐨勮В绋辩偤( )
A锛庡熀鏈В B锛庡熀鏈彲琛岃В C锛庡彲琛岃В D锛庢渶鍎�(y艒u)瑙�
2. 绶氭€ц(gu墨)鍔冨彲琛屽煙鐨勯爞榛炰竴瀹氭槸( )
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3. X 鏄窔鎬ц(gu墨)鍔冪殑鍩烘湰鍙瑙ｅ墖鏈�( )
A锛嶺 涓殑鍩鸿畩閲忛潪璨�锛岄潪鍩鸿畩閲忕偤闆� B锛嶺 鏄渶鍎�(y艒u)瑙�
C锛嶺 涓嶄竴瀹氭豢瓒崇磩鏉熸浠� D锛嶺 涓殑鍩鸿畩閲忛潪闆讹紝闈炲熀璁婇噺鐐洪浂
4. 绶氭€ц(gu墨)鍔冩渶鍎�(y艒u)瑙ｅ敮涓€鏄寚( )
A锛庡彲琛岃В闆嗗悎鐒＄晫 B锛庢渶鍎�(y艒u)琛ㄤ腑瀛樺湪闈炲熀璁婇噺鐨勬椹楁暩(sh霉)鐐洪浂
C锛庡彲琛岃В闆嗗悎鏄┖闆� D锛庢渶鍎�(y艒u)琛ㄤ腑闈炲熀璁婇噺鐨勬椹楁暩(sh霉)鍏ㄥぇ浜庨浂
5. 鍘熷晱椤屾湁 4 鍊嬭畩閲� 3 鍊嬬磩鏉�锛屽叾灏嶅伓鍟忛( )
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C锛庢湁 4 鍊嬭畩閲� 3 鍊嬬磩鏉� D锛庢湁 4 鍊嬭畩閲� 4 鍊嬬磩鏉�
6. 鍦ㄩ亱杓稿晱椤屼腑锛屾瘡娆¤凯浠ｆ檪锛屽鏋滄湁鏌愰潪鍩鸿畩閲忕殑妾㈤鏁�(sh霉)绛変簬闆讹紝鍓囪┎閬�
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7. 灏嶅伓鍠磾褰㈡硶涓紝鑻ユ豢瓒�( )锛屽墖鍘熷晱椤屾矑鏈夊彲琛岃В銆�
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B锛庢椹楁暩(sh霉)涓嚭鐝�(xi脿n)姝ｆ暩(sh霉)
C锛庢椹楁暩(sh霉)鍏ㄩ儴灏忎簬闆�
D锛庡瓨鍦ㄦ煇鍊嬪熀璁婇噺鐐鸿矤鏁�(sh霉)锛屼笖鍏舵墍鍦ㄨ鐨勭郴鏁�(sh霉)鍏ㄩ儴澶т簬鎴栫瓑浜庨浂
8. 鑻ユü T 鏈� n 鍊嬮爞榛烇紝閭ｄ箞瀹冪殑閭婃暩(sh霉)涓€瀹氭槸( )
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9. 鍘熷晱椤岃垏灏嶅伓鍟忛閮芥湁鍙瑙�锛屽墖鏈�( )
A銆佸師鍟忛鏈夋渶鍎�(y艒u)瑙ｏ紝灏嶅伓鍟忛鍙兘娌掓湁鏈€鍎�(y艒u)瑙�
B銆佸師鍟忛鑸囧皪鍋跺晱椤屽彲鑳介兘娌掓湁鏈€鍎�(y艒u)瑙�
C銆佸彲鑳戒竴鍊嬪晱椤屾湁鏈€鍎�(y艒u)瑙�锛屽彟涓€鍊嬪晱椤屽叿鏈夌劇鐣岃В
D銆佸師鍟忛鑸囧皪鍋跺晱椤岄兘鍏锋湁鏈€鍎�(y艒u)瑙�
10.鐢ㄥ壊骞抽潰娉曟眰瑙ｆ暣鏁�(sh霉)瑕�(gu墨)鍔冩檪锛屾(g貌u)閫犵殑鍓插钩闈㈠彧鑳藉垏鍘�( )
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锛堜簩锛夊～绌洪锛堟瘡绌烘牸 2 鍒�锛屽叡 20 鍒嗭級
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鎴栧彇闆堕兘鍙互锛屽墖绋� xj 鐐� 銆�
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b (i=1,鈥�,m)锛�
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鍊�銆� 銆� 鍜屽彸绔父鏁�(sh霉)闋呴兘闈炶矤銆�
5. 妯归€ｉ€�锛屼絾涓嶅瓨鍦� 銆�
6. 濡傛灉鏌愪竴鏁存暩(sh霉)瑕�(gu墨)鍔冿細
绗� 5 闋�锛屽叡 7 闋�
Min Z=-7X1-9X2
-X1 +3X2 鈮� 6
7X1 + X2 鈮� 35
X1, X2 鈮� 0 涓斿潎鐐烘暣鏁�(sh霉)
鎵€灏嶆噳(y墨ng)鐨勭窔鎬ц(gu墨)鍔冿紙鏉惧紱鍟忛锛夌殑鏈€鍎�(y艒u)瑙ｇ偤 X1=9/2锛孹2=7/2锛孧in Z=-63锛屾垜
鍊戠従(xi脿n)鍦ㄨ灏� X1 閫茶鍒嗘灊锛屾噳(y墨ng)瑭插垎鐐� 鍜� 銆�
7. 姹傝В闈炶矤璩︽瑠(qu谩n)鍦栫殑鏈€鐭矾寰戝晱椤岀殑杓冨ソ绠楁硶鏄� 銆�
锛堜笁锛夌啊绛旈锛堝叡 3 灏忛锛屾瘡椤� 5 鍒�锛屽叡 15 鍒嗭級
1. 绶氭€ц(gu墨)鍔冨彧瑕佹湁鍙瑙ｄ竴瀹氭湁鍩烘湰鍙瑙�銆傞偅涔�锛岃兘鍚︾⒑瀹氫竴瀹氬瓨鍦ㄦ渶鍎�(y艒u)
瑙�锛�
2. 宸茬煡鍘熷晱椤屾湁鏈€鍎�(y艒u)瑙�锛岄偅涔堝皪鍋跺晱椤屽憿锛熷畠鍊戠殑浠€涔堟槸鐩哥瓑鐨勶紵
3. 鐐轰粈涔堣浠讳竴閬嬭几缍�(w菐ng)绲�(lu貌)涓嚦灏戝瓨鍦ㄤ竴鍊嬪彲琛屾祦锛�
锛堝洓锛夊缓妯￠锛堝叡 2 灏忛锛屾瘡椤� 10 鍒�锛屽叡 20 鍒嗭級
1. 涓€鍊嬭粖闁撹鍔犲伐 3 绋浂浠讹紝鍏堕渶瑕侀噺鍒嗗垾鐐� 4000 浠�銆�5000 浠跺拰 3500 浠�. 杌�
闁撳収(n猫i)鐝�(xi脿n)鏈� 4 鑷烘搴�锛岄兘鍙敤渚嗗姞宸ラ€� 3 绋浂浠讹紝姣忚嚭姗熷簥鍙埄鐢ㄧ殑宸ユ檪鍒嗗垾鐐� 1600,
1250, 1800 鍜� 2000. 姗熷簥 i#
鍔犲伐闆朵欢 j#
鎵€闇€宸ユ檪鍜屾垚鏈敱琛� 1 绲﹀嚭锛屽晱濡備綍瀹夋帓鐢�
鐢�(ch菐n)锛屾墠鑳戒娇鐢熺敘(ch菐n)鎴愭湰鏈€浣�锛岃珛鍒楀嚭鏁�(sh霉)瀛�(xu茅)妯″瀷锛屼笉闇€瑕佹眰瑙�銆�
琛� 1
2. 瀵嚭涓嬪垪绶氭€ц(gu墨)鍔冨晱椤岀殑灏嶅伓鍟忛锛�
绗� 6 闋�锛屽叡 7 闋�
Max f =3x1 -2x2-5x3-8x5;
s.t. 2x1 +3x2 -3x3- x4 -5x5 鈮�-2,
x2 -2x3+3x4 +4x5 =-5,
-x1 +2x3 -2x4 -3x5 鈮�-5.
x1 鈮� 0, x2 鐒＄磩鏉�, x3鈮� 0, x4鈮� 0, x5 鐒＄磩鏉�.
锛堜簲锛夎▓绠楅锛堝叡 5 灏忛锛屾瘡椤� 15 鍒嗭級
1. 鐢ㄥ柈绱斿舰娉曟眰瑙ｄ笅鍒楃窔鎬ц(gu墨)鍔冨晱椤岋細
min f =-5x1 -4x2;
s.t. x1 + 2x2 鈮�6,
2x1 -x2 鈮�4,
5x1 +3x2 鈮�15,
x1 鈮� 0, x2 鈮� 0.
2. 姹傝В琛� 2 鎵€绲﹂亱杓稿晱椤岋細
(1) 鐢ㄨタ鍖楄娉曟眰鍒濆瑙�锛�
(2) 鐢ㄤ綅鍕㈡硶姹傛渶鍎�(y艒u)瑙�銆�
琛� 2
3. 鐢ㄥ壊骞抽潰娉曟眰瑙ｄ笅鍒楁暣鏁�(sh霉)瑕�(gu墨)鍔冿細
min f =-3x1 -4x2;
s.t. 2x1 +5x2 +x3 = 15,
2x1 -2x2 +x4 = 5,
绗� 7 闋�锛屽叡 7 闋�
xj 鈮� 0, 鏁存暩(sh霉), j=1,2,3,4.
宸茬煡鐩告噳(y墨ng)鐨�(LP)鐨勬渶鍎�(y艒u)鍠磾褰㈣〃濡傝〃 3 鎵€绀恒€�
琛� 3
XB x1 x2 x3 x4 b
x2 0 1 1/7 -1/7 10/7
x1 1 0 1/7 5/14 55/14
r 0 0 1 1/2 35/2
4. 姹傚湒 1 涓� v1 鑷� v10 鐨勬渶鐭矾寰戝拰闀峰害銆�
鍦� 1
5. 姹傞亱杓哥恫(w菐ng)绲�(lu貌)鍦栧湒 2 鐨勬渶澶ф祦鍙婃渶灏忓壊銆�
鍦� 2
鍏嶈铂(z茅)鑱叉槑锛氭湰鏂囩郴杞�(zhu菐n)杓夎嚜缍�(w菐ng)绲�(lu貌)锛屽鏈変镜鐘紝璜嬭伅(li谩n)绯绘垜鍊戠珛鍗冲埅闄�锛屽彟锛氭湰鏂囧儏浠ｈ〃浣滆€呭€嬩汉瑙€榛烇紝鑸囨湰缍�(w菐ng)绔欑劇闂�(gu膩n)銆傚叾鍘熷壍(chu脿ng)鎬т互鍙婃枃涓櫝杩版枃瀛楀拰鍏�(n猫i)瀹规湭缍�(j墨ng)鏈珯璀夊锛屽皪鏈枃浠ュ強鍏朵腑鍏ㄩ儴鎴栬€呴儴鍒嗗収(n猫i)瀹�銆佹枃瀛楃殑鐪熷鎬�銆佸畬鏁存€�銆佸強鏅傛€ф湰绔欎笉浣滀换浣曚繚璀夋垨鎵胯锛岃珛璁€鑰呭儏浣滃弮鑰冿紝骞惰珛鑷鏍稿鐩搁棞(gu膩n)鍏�(n猫i)瀹�銆�
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鏂囩珷鎼滅储
鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
