某工程机械厂根据市场需求，计划生产A、B两型号的大型挖掘机共100台，该厂所筹生产资金不少于22400万元，
\u67d0\u5de5\u7a0b\u673a\u68b0\u5382\u6839\u636e\u5e02\u573a\u9700\u6c42,\u8ba1\u5212\u751f\u4ea7A\u3001B\u4e24\u578b\u53f7\u7684\u5927\u578b\u6316\u6398\u673a\u5171100\u53f0\uff0c\u8be5\u5382\u6240\u7b79\u751f\u4ea7\u8d44\u91d1\u4e0d\u5c11\u4e8e22400\u4e07\u5143.\uff081\uff09\uff0c\u8bbe\u751f\u4ea7A\u578b\u53f7\u6316\u6398\u673aa\u53f0\uff0cB\u578b\u53f7\u6316\u6398\u673ab\u53f0\uff08a\uff0cb\u2208\u81ea\u7136\u6570N\uff09\u3002\u5219\u6709a+b=100\uff0c\u5373b=100-a
\u90a3\u4e48 22400\u2264200a+240b\u226422500\uff0c\u537322400\u2264200a+240\uff08100-a\uff09\u226422500
22400\u226424000-40a\u226422500\uff0c\u89e3\u4e0d\u7b49\u5f0f\u7ec4\uff0c\u5f97a\u2208\u301037.5\uff0c40\u3011
\u2235 a\u2208N \u2234a1=38\uff0ca2=39\uff0ca3=40
\u90a3\u4e48\u76f8\u5bf9\u5e94\u7684\uff0cb1=62\uff0cb2=61\uff0cb3=60\u3002
\u6240\u4ee5\uff0c\u8be5\u5382\u5171\u67093\u5957\u751f\u4ea7\u65b9\u6848\uff0c\u5206\u522b\u662f\u751f\u4ea7A\u578b\u53f738\u53f0\uff0cB\u578b\u53f762\u53f0\uff1b\u751f\u4ea7A\u578b\u53f739\u53f0\uff0cB\u578b\u53f761\u53f0\uff1b\u751f\u4ea7A\u578b\u53f740\u53f0\uff0cB\u578b\u53f760\u53f0\u3002
\uff082\uff09\u751f\u4ea7A\u578b\u53f7\u6316\u6398\u673a\u7684\u5229\u6da6\u662f250-200=50\uff08\u4e07\u5143\uff09\uff0c\u751f\u4ea7B\u578b\u53f7\u6316\u6398\u673a\u7684\u5229\u6da6\u662f300-240=60\uff08\u4e07\u5143\uff09
\u663e\u7136\uff0c\u5728\u603b\u6570\u4e3a100\u53f0\u4e0d\u53d8\u7684\u60c5\u51b5\u4e0b\uff0c\u751f\u4ea7B\u578b\u53f7\u6316\u6398\u673a\u8d8a\u591a\uff0c\u5229\u6da6\u8d8a\u5927\u3002
\u90a3\u4e48\uff0c\u5728\u751f\u4ea7A\u578b\u53f7\u6316\u6398\u673a38\u53f0\uff0cB\u578b\u53f7\u6316\u6398\u673a62\u53f0\u7684\u60c5\u51b5\u4e0b\uff0c\u8be5\u5382\u53ef\u83b7\u6700\u5927\u5229\u6da6\u3002\u5229\u6da6\u989d\u4e3a50*38+60*62=5620\uff08\u4e07\u5143\uff09
\uff083\uff09\u5f53A\u578b\u53f7\u6316\u6398\u673a\u7684\u552e\u4ef7\u4e0a\u6da8m\u4e07\u5143\uff08m\uff1e0\uff09\u65f6\uff0c\u751f\u4ea7A\u578b\u53f7\u7684\u5229\u6da6\u4e3a\uff08250+m-200\uff09=50+m\uff08\u4e07\u5143\uff09
\u4ee4\u5229\u6da6\u6700\u5927\u65f6\uff0c\u751f\u4ea7A\u578b\u53f7\u6316\u6398\u673aa\u53f0\uff0c\u90a3\u4e48\u751f\u4ea7B\u578b\u53f7\u6316\u6398\u673a\uff08100-a\uff09\u53f0 \uff08a\u2208\u301038\uff0c40\u3011\uff0ca\u2208N\uff09
\u6b64\u65f6\u603b\u552e\u4ef7\u4e3a\uff08250+m\uff09a+300\uff08100-a\uff09=\uff08m-50\uff09a+30000
\u603b\u6210\u672c\u4e3a200a+240\uff08100-a\uff09=24000-40a
\u5229\u6da6\u4e3a\uff08m-50\uff09a+30000-\uff0824000-40a\uff09=\uff08m-10\uff09a+6000\uff08a\u2208\u301038\uff0c40\u3011\uff0cm\uff1e0 \uff09
\u4e3a\u4f7f\u5229\u6da6\u6700\u5927\uff0c\u4ee5\u4e0b\u5206\u60c5\u51b5\u8ba8\u8bba
1\u00b0 \u5f530\uff1cm\uff1c10\u65f6\uff0c\u5219m-10\uff1c0\uff0c\u90a3\u4e48\u4e3a\u4f7f\u5229\u6da6\u6700\u5927\uff0c\u5219a\u5e94\u53d6\u5f97\u6700\u5c0f\u503c\uff0c\u5373a=38
\u90a3\u4e48\uff0c\u8be5\u5382\u5e94\u751f\u4ea7A\u578b\u53f7\u6316\u6398\u673a38\u53f0\uff0cB\u578b\u53f7\u6316\u6398\u673a62\u53f0\u3002
2\u00b0 \u5f53m=10\u65f6\uff0c\u5219m-10=0\uff0c\u90a3\u4e48\u5229\u6da6\u4e3a6000\u4e07\u5143\uff0c\u4e0ea\u65e0\u5173\u3002
\u90a3\u4e48\uff0c\u8be5\u5382\u53ef\u4ece\uff081\uff09\u9898\u76843\u79cd\u65b9\u6848\u5185\u4efb\u9009\u4e00\u79cd\u65b9\u6848\u8fdb\u884c\u751f\u4ea7\u3002
3\u00b0 \u5f53m\uff1e10\u65f6\uff0c\u5219m-10\uff1e0\uff0c\u90a3\u4e48\u4e3a\u4f7f\u5229\u6da6\u6700\u5927\uff0c\u5219a\u5e94\u53d6\u5230\u6700\u5927\u503c\uff0c\u5373a=40
\u90a3\u4e48\uff0c\u8be5\u5382\u5e94\u751f\u4ea7A\u578b\u53f7\u6316\u6398\u673a40\u53f0\uff0cB\u578b\u53f7\u6316\u6398\u673a60\u53f0\u3002
\uff081\uff09\uff0c\u8bbe\u751f\u4ea7A\u578b\u53f7\u6316\u6398\u673aa\u53f0\uff0cB\u578b\u53f7\u6316\u6398\u673ab\u53f0\uff08a\uff0cb\u2208\u81ea\u7136\u6570N\uff09\u3002\u5219\u6709a+b=100\uff0c\u5373b=100-a
\u90a3\u4e48 22400\u2264200a+240b\u226422500\uff0c\u537322400\u2264200a+240\uff08100-a\uff09\u226422500
22400\u226424000-40a\u226422500\uff0c\u89e3\u4e0d\u7b49\u5f0f\u7ec4\uff0c\u5f97a\u2208\u301037.5\uff0c40\u3011
\u2235 a\u2208N \u2234a1=38\uff0ca2=39\uff0ca3=40
\u90a3\u4e48\u76f8\u5bf9\u5e94\u7684\uff0cb1=62\uff0cb2=61\uff0cb3=60\u3002
\u6240\u4ee5\uff0c\u8be5\u5382\u5171\u67093\u5957\u751f\u4ea7\u65b9\u6848\uff0c\u5206\u522b\u662f\u751f\u4ea7A\u578b\u53f738\u53f0\uff0cB\u578b\u53f762\u53f0\uff1b\u751f\u4ea7A\u578b\u53f739\u53f0\uff0cB\u578b\u53f761\u53f0\uff1b\u751f\u4ea7A\u578b\u53f740\u53f0\uff0cB\u578b\u53f760\u53f0\u3002
\uff082\uff09\u751f\u4ea7A\u578b\u53f7\u6316\u6398\u673a\u7684\u5229\u6da6\u662f250-200=50\uff08\u4e07\u5143\uff09\uff0c\u751f\u4ea7B\u578b\u53f7\u6316\u6398\u673a\u7684\u5229\u6da6\u662f300-240=60\uff08\u4e07\u5143\uff09
\u663e\u7136\uff0c\u5728\u603b\u6570\u4e3a100\u53f0\u4e0d\u53d8\u7684\u60c5\u51b5\u4e0b\uff0c\u751f\u4ea7B\u578b\u53f7\u6316\u6398\u673a\u8d8a\u591a\uff0c\u5229\u6da6\u8d8a\u5927\u3002
\u90a3\u4e48\uff0c\u5728\u751f\u4ea7A\u578b\u53f7\u6316\u6398\u673a38\u53f0\uff0cB\u578b\u53f7\u6316\u6398\u673a62\u53f0\u7684\u60c5\u51b5\u4e0b\uff0c\u8be5\u5382\u53ef\u83b7\u6700\u5927\u5229\u6da6\u3002\u5229\u6da6\u989d\u4e3a50*38+60*62=5620\uff08\u4e07\u5143\uff09
\uff083\uff09\u5f53A\u578b\u53f7\u6316\u6398\u673a\u7684\u552e\u4ef7\u4e0a\u6da8m\u4e07\u5143\uff08m\uff1e0\uff09\u65f6\uff0c\u751f\u4ea7A\u578b\u53f7\u7684\u5229\u6da6\u4e3a\uff08250+m-200\uff09=50+m\uff08\u4e07\u5143\uff09
\u4ee4\u5229\u6da6\u6700\u5927\u65f6\uff0c\u751f\u4ea7A\u578b\u53f7\u6316\u6398\u673aa\u53f0\uff0c\u90a3\u4e48\u751f\u4ea7B\u578b\u53f7\u6316\u6398\u673a\uff08100-a\uff09\u53f0 \uff08a\u2208\u301038\uff0c40\u3011\uff0ca\u2208N\uff09
\u6b64\u65f6\u603b\u552e\u4ef7\u4e3a\uff08250+m\uff09a+300\uff08100-a\uff09=\uff08m-50\uff09a+30000
\u603b\u6210\u672c\u4e3a200a+240\uff08100-a\uff09=24000-40a
\u5229\u6da6\u4e3a\uff08m-50\uff09a+30000-\uff0824000-40a\uff09=\uff08m-10\uff09a+6000\uff08a\u2208\u301038\uff0c40\u3011\uff0cm\uff1e0 \uff09
\u4e3a\u4f7f\u5229\u6da6\u6700\u5927\uff0c\u4ee5\u4e0b\u5206\u60c5\u51b5\u8ba8\u8bba
1\u00b0 \u5f530\uff1cm\uff1c10\u65f6\uff0c\u5219m-10\uff1c0\uff0c\u90a3\u4e48\u4e3a\u4f7f\u5229\u6da6\u6700\u5927\uff0c\u5219a\u5e94\u53d6\u5f97\u6700\u5c0f\u503c\uff0c\u5373a=38
\u90a3\u4e48\uff0c\u8be5\u5382\u5e94\u751f\u4ea7A\u578b\u53f7\u6316\u6398\u673a38\u53f0\uff0cB\u578b\u53f7\u6316\u6398\u673a62\u53f0\u3002
2\u00b0 \u5f53m=10\u65f6\uff0c\u5219m-10=0\uff0c\u90a3\u4e48\u5229\u6da6\u4e3a6000\u4e07\u5143\uff0c\u4e0ea\u65e0\u5173\u3002
\u90a3\u4e48\uff0c\u8be5\u5382\u53ef\u4ece\uff081\uff09\u9898\u76843\u79cd\u65b9\u6848\u5185\u4efb\u9009\u4e00\u79cd\u65b9\u6848\u8fdb\u884c\u751f\u4ea7\u3002
3\u00b0 \u5f53m\uff1e10\u65f6\uff0c\u5219m-10\uff1e0\uff0c\u90a3\u4e48\u4e3a\u4f7f\u5229\u6da6\u6700\u5927\uff0c\u5219a\u5e94\u53d6\u5230\u6700\u5927\u503c\uff0c\u5373a=40
\u90a3\u4e48\uff0c\u8be5\u5382\u5e94\u751f\u4ea7A\u578b\u53f7\u6316\u6398\u673a40\u53f0\uff0cB\u578b\u53f7\u6316\u6398\u673a60\u53f0\u3002
由“该厂所筹生产资金不少于22400万元，但不超过22500万元”和表中生产成本可得：
22400≤200x+240（100-x）≤22500，
37.5≤x≤40，
∵x为整数，
∴x取值为38、39、40．
故有三种生产方案．
即：第一种方案：生产A型挖掘机38台，生产B型挖掘机62台；
第二种方案：生产A型挖掘机39台，生产B型挖掘机61台；
第三种方案：生产A型挖掘机40台，生产B型挖掘机60台．
（2）三种方案获得的利润分别为：
第一种方案：38×（250-200）+62×（300-240）=5620；
第二种方案：39×（250-200）+61×（300-240）=5610；
第三种方案：40×（250-200）+60×（300-240）=5600．
故生产A型挖掘机38台，生产B型挖掘机62台的方案获得利润最大．
绛旓細瑙ｏ細璁句拱A x鍙 B (100-x)鍙 22400<=200x+250(100-x)<=22500 50<=x<=52 x=50銆51銆52 鍒╂鼎w=40*x+(50+M)*(100-x)= -(10+M)*x+100*(50+M)褰搙=50鏃讹紝鍒╂鼎w鏈澶=4500+50M 鏂规锛欰銆丅鍚50鍙
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绛旓細1 鍥犱负|5x-8|=8-5x,鎵浠5x-8灏忎簬绛変簬0 鎵浠ュ緱x灏忎簬绛変簬8/5 甯屾湜閲囩撼
绛旓細璁句拱A x鍙 B (100-x)鍙 22400<=200x+250(100-x)<=22500 50<=x<=52 x=50銆51銆52 鍒╂鼎w=40*x+(50+M)*(100-x)= -(10+M)*x+100*(50+M)褰搙=50鏃讹紝鍒╂鼎w鏈澶=4500+50M 鏂规锛欰銆丅鍚50鍙 绛旓細鐣
绛旓細1 16 =500/10/3 2 閿鍞600浠朵互锛岀浜岀鏂规鍒╂鼎澶э紱瓒呰繃600浠讹紝绗竴绉嶆柟妗堝埄娑﹀ぇ 3 鍏辨湁113绉嶆柟妗堛傛渶澶у埄娑︽柟妗堟湁19绉嶏紝濡備笅锛欰 B 2 92 8 87 14 82 20 77 26 72 32 67 38 62 44 57 50 52 56 47 62 42 68 37 74 32 80 27 86 22 92 17 98 12 104 7 110 2 ...
绛旓細瑙ｏ紝(1)渚濋鎰忥紝璁続鎸栨帢鏈虹殑鍙版暟涓篈锛孊鎸栨帢鏈虹殑鍙版暟涓築 鍒欐湁锛孉+B=100锛200A+240B鈮22400 鍥犳鏈堿鈮40鍙帮紝B鈮60鍙 (2)鏂规1锛岀敓浜40鍙帮紝B60鍙帮紝璧勯噾鍒氬ソ鐢ㄥ畬 鏂规2锛岀敓浜+B锛100鍙帮紱A锛40鍙帮紝B锛60鍙帮紝瑕佺闆嗘洿澶氳祫閲 鏂规3锛岀敓浜+B锛100鍙帮紱A锛40鍙帮紝B锛60鍙帮紝璧勯噾浼氭湁...
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绛旓細璁句拱A x鍙 B (100-x)鍙 22400<=200x+250(100-x)<=22500 50<=x<=52 x=50銆51銆52 鍒╂鼎w=40*x+(50+M)*(100-x)= -(10+M)*x+100*(50+M)褰搙=50鏃讹紝鍒╂鼎w鏈澶=4500+50M 鏂规锛欰銆丅鍚50鍙 绛旓細鐣
绛旓細1/[1/15*锛1+20%锛塢=1/[1/15*1.2]=1/[1/8]=8澶 锛5/6-1/16*4锛/锛1/16+1/12锛=7/12/锛7/48锛=4澶
