ÄÚÈÝ·¢²¼¸üÐÂʱ¼ä : 2025/5/30 12:00:57ÐÇÆÚÒ» ÏÂÃæÊÇÎÄÕµÄÈ«²¿ÄÚÈÝÇëÈÏÕæÔĶÁ¡£
(3)ÓÉÓÚÔ¤ËãÏß·½³ÌµÄÒ»°ãÐÎʽΪP1X1£«P2X2£½M
ËùÒÔ£¬ÓÉ(1)¡¢(2)¿É½«Ô¤ËãÏß·½³Ì¾ßÌåдΪ£º2X1£«3X2£½60¡£
22
(4)½«(3)ÖеÄÔ¤ËãÏß·½³Ì½øÒ»²½ÕûÀíΪX2£½£X1£«20¡£ºÜÇå³þ£¬Ô¤ËãÏßµÄбÂÊΪ£¡£
33
(5)ÔÚÏû·ÑÕßЧÓÃ×î´ó»¯µÄ¾ùºâµãEÉÏ£¬ÓÐMRS12£½£¬¼´ÎÞ²îÒìÇúÏßбÂʵľø¶ÔÖµ¼´MRSµÈÓÚÔ¤ËãÏßб
P1
P2
P1P12
Âʵľø¶ÔÖµ¡£Òò´Ë£¬MRS12£½£½¡£
P2P23
3.½â´ð£º(1)¸ù¾ÝÌâÒ⣬¶ÔÏû·ÑÕßA¶øÑÔ£¬ÈȲèÊÇÖÐÐÔÉÌÆ·£¬Òò´Ë£¬ÈȲèµÄÏû·ÑÊýÁ¿²»»áÓ°ÏìÏû·ÑÕßAµÄЧÓÃˮƽ¡£Ïû·ÑÕßAµÄÎÞ²îÒìÇúÏß¼ûͼ3¡ª2(a)¡£Í¼3¡ª2ÖеļýÍ·¾ù±íʾЧÓÃˮƽÔö¼ÓµÄ·½Ïò¡£
(2)¸ù¾ÝÌâÒ⣬¶ÔÏû·ÑÕßB¶øÑÔ£¬¿§·ÈºÍÈȲèÊÇÍêÈ«»¥²¹Æ·£¬ÆäЧÓú¯ÊýÊÇU£½min{x1£¬x2}¡£Ïû·ÑÕßBµÄÎÞ²îÒìÇúÏß¼ûͼ3¡ª2(b)¡£
(3)¸ù¾ÝÌâÒ⣬¶ÔÏû·ÑÕßC¶øÑÔ£¬¿§·ÈºÍÈȲèÊÇÍêÈ«Ìæ´úÆ·£¬ÆäЧÓú¯ÊýÊÇU£½2x1£«x2¡£Ïû·ÑÕßCµÄÎÞ²îÒìÇúÏß¼ûͼ3¡ª2(c)¡£
(4)¸ù¾ÝÌâÒ⣬¶ÔÏû·ÑÕßD¶øÑÔ£¬¿§·ÈÊÇÑá¶ñÆ·¡£Ïû·ÑÕßDµÄÎÞ²îÒìÇúÏß¼ûͼ3¡ª2(d)¡£
ͼ3¡ª2 ¹ØÓÚ¿§·ÈºÍÈȲèµÄ²»Í¬Ïû·ÑÕßµÄÎÞ²îÒìÇúÏß
4.
ͼ3¡ª3
½â´ð£ºÒ»°ã˵À´£¬·¢¸øÏû·ÑÕßÏÖ½ð²¹Öú»áʹÏû·ÑÕß»ñµÃ¸ü´óµÄЧÓá£ÆäÔÒòÔÚÓÚ£ºÔÚÏÖ½ð²¹ÖúµÄÇé¿öÏ£¬Ïû·ÑÕß¿ÉÒÔ°´ÕÕ×Ô¼ºµÄÆ«ºÃÀ´¹ºÂòÉÌÆ·£¬ÒÔ»ñµÃ¾¡¿ÉÄÜ´óµÄЧÓá£Èçͼ3¡ª3Ëùʾ¡£
ÔÚͼ3¡ª3ÖУ¬Ö±ÏßABÊǰ´ÊµÎï²¹ÖúÕÛËãµÄ»õ±ÒÁ¿¹¹³ÉµÄÏÖ½ð²¹ÖúÇé¿öϵÄÔ¤ËãÏß¡£ÔÚÏÖ½ð²¹ÖúµÄÔ¤Ëã
**
ÏßABÉÏ£¬Ïû·ÑÕ߸ù¾Ý×Ô¼ºµÄÆ«ºÃÑ¡ÔñÉÌÆ·1ºÍÉÌÆ·2µÄ¹ºÂòÁ¿·Ö±ðΪx1ºÍx2£¬´Ó¶øÊµÏÖÁË×î´óµÄЧÓÃˮƽU2£¬¼´ÔÚͼ3¡ª3ÖбíÏÖΪԤËãÏßABºÍÎÞ²îÒìÇúÏßU2ÏàÇеľùºâµãE¡£
¶øÔÚʵÎï²¹ÖúµÄÇé¿öÏ£¬Ôòͨ³£²»»á´ïµ½×î´óµÄЧÓÃˮƽU2¡£ÒòΪ£¬Æ©È磬µ±ÊµÎï²¹ÖúµÄÉÌÆ·×éºÏΪF
9
µã(¼´Á½ÉÌÆ·ÊýÁ¿·Ö±ðΪx11¡¢x21)£¬»òÕßΪGµã(¼´Á½ÉÌÆ·ÊýÁ¿·Ö±ðΪx12ºÍx22)ʱ£¬ÔòÏû·ÑÕßÄÜ»ñµÃÎÞ²îÒìÇúÏßU1Ëù±íʾµÄЧÓÃˮƽ£¬ÏÔÈ»£¬U1 MU1P1 5.½â´ð£º¸ù¾ÝÏû·ÑÕßµÄЧÓÃ×î´ó»¯µÄ¾ùºâÌõ¼þ £½ MU2P2 dTUdTU22 ÆäÖУ¬ÓÉU£½3X1X2¿ÉµÃMU1£½£½3X2 MU2£½£½6X1X2 dX1dX2 2 3X220 ÓÚÊÇ£¬ÓÐ £½ 6X1X2304 ÕûÀíµÃ X2£½X1 (1) 3 4 ½«Ê½(1)´úÈëÔ¤ËãÔ¼ÊøÌõ¼þ20X1£«30X2£½540£¬µÃ20X1£«30¡¤X1£½540 3 ½âµÃ X1£½9 ½«X1£½9´úÈëʽ(1)µÃX2£½12 Òò´Ë£¬¸ÃÏû·ÑÕßÿÄ깺ÂòÕâÁ½ÖÖÉÌÆ·µÄÊýÁ¿Ó¦¸ÃΪ X1=9£¬X2=12 ***22 ½«ÒÔÉÏ×îÓŵÄÉÌÆ·×éºÏ´úÈëЧÓú¯Êý£¬µÃU£½3X1(X2)£½3¡Á9¡Á12£½3 888 Ëü±íÃ÷¸ÃÏû·ÑÕßµÄ×îÓÅÉÌÆ·¹ºÂò×éºÏ¸øËû´øÀ´µÄ×î´óЧÓÃˮƽΪ3 888¡£ d 6. ½â´ð£º(1)ÓÉÏû·ÑÕßAµÄÐèÇóº¯ÊýQA£½20£4P£¬¿É±àÖÆÏû·ÑÕßAµÄÐèÇó±í£»ÓÉÏû·ÑÕßBµÄÐèÇóº¯Êýd QB£½30£5P£¬¿É±àÖÆÏû·ÑBµÄÐèÇó±í¡£ÖÁÓÚÊг¡µÄÐèÇó±íµÄ±àÖÆ¿ÉÒÔʹÓÃÁ½ÖÖ·½·¨£¬Ò»ÖÖ·½·¨ÊÇÀûÓÃÒѵõ½Ïû·ÑÕßA¡¢BµÄÐèÇó±í£¬½«Ã¿Ò»¼Û¸ñˮƽÉÏÁ½¸öÏû·ÑÕßµÄÐèÇóÊýÁ¿¼Ó×ÜÀ´±àÖÆÊг¡ÐèÇó±í£»ÁíÒ»ÖÖ·½·¨ÊÇÏÈ ddd½«Ïû·ÑÕßAºÍBµÄÐèÇóº¯Êý¼Ó×ÜÀ´ÇóµÃÊг¡ÐèÇóº¯Êý£¬¼´Êг¡ÐèÇóº¯ÊýQ£½QA£«QB£½(20£4P)£«(30£5P)£½ d50£9P£¬ È»ºóÔËÓÃËùµÃµ½µÄÊг¡ÐèÇóº¯ÊýQ£½50£9PÀ´±àÖÆÊг¡ÐèÇó±í¡£ÕâÁ½ÖÖ·½·¨ËùµÃµ½µÄÊг¡ÐèÇó±íÊÇÏàͬµÄ¡£°´ÒÔÉÏ·½·¨±àÖÆµÄ3ÕÅÐèÇó±íÈçÏÂËùʾ¡£ Ïû·ÑÕßAµÄÐèÇó±í dP QA 0 20 1 16 2 12 3 8 4 4 5 0 ,Ïû·ÑÕßBµÄÐèÇó±í dP QB 0 30 1 25 2 20 3 15 4 10 5 5 6 0 ,Êг¡µÄÐèÇó±í dP Q£½50£9P 0 50 1 41 2 32 3 23 4 14 5 5 10 6 0 11 (2)ÓÉ(1)ÖеÄ3ÕÅÐèÇó±í£¬Ëù»³öµÄÏû·ÑÕßAºÍB¸÷×ÔµÄÐèÇóÇúÏßÒÔ¼°Êг¡µÄÐèÇóÇúÏßÈçͼ3¡ª4Ëùʾ¡£ ͼ3¡ª4 d ÔÚ´Ë£¬ÐèÒªÌØ±ðÖ¸³öµÄÊÇ£¬Êг¡ÐèÇóÇúÏßÓÐÒ»¸öÕ۵㣬¸Ãµã·¢ÉúÔÚ¼Û¸ñP£½5ºÍÐèÇóÁ¿Q£½5µÄ×ø±êµãλÖ᣹ØÓÚÊг¡ÐèÇóÇúÏßµÄÕâÒ»ÌØÕ÷£¬¿ÉÒÔ´ÓÁ½¸ö½Ç¶ÈÀ´½âÊÍ£ºÒ»¸ö½Ç¶ÈÊÇ´ÓͼÐÎÀ´Àí½â£¬Êг¡ÐèÇóÇúÏßÊÇÊг¡Éϵ¥¸öÏû·ÑÕßÐèÇóÇúÏßµÄˮƽ¼Ó×Ü£¬¼´ÔÚP¡Ü5µÄ·¶Î§£¬Êг¡ÐèÇóÇúÏßÓÉÁ½¸öÏû·ÑÕßÐèÇóÇúÏßˮƽ¼Ó×ܵõ½£»¶øµ±P£¾5ʱ£¬Ö»ÓÐÏû·ÑÕßBµÄÐèÇóÇúÏß·¢Éú×÷Óã¬ËùÒÔ£¬ËûµÄÐèÇóÇúÏß¾ÍÊÇÊг¡ÐèÇóÇúÏß¡£ÁíÒ»¸ö ddd½Ç¶ÈÊÇ´ÓÐèÇóº¯Êý¿´£¬ÔÚP¡Ü5µÄ·¶Î§£¬Êг¡ÐèÇóº¯ÊýQ£½QA£«QB£½(20£4P)£«(30£5P)£½50£9P³ÉÁ¢£»¶ø dd µ±P£¾5ʱ£¬Ö»ÓÐÏû·ÑÕßBµÄÐèÇóº¯Êý²Å¹¹³ÉÊг¡ÐèÇóº¯Êý£¬¼´Q£½QB£½30£5P¡£ 7¡¢½â´ð£º¸ù¾ÝÏû·ÑÕßЧÓÃ×î´ó»¯µÄ¾ùºâÌõ¼þMU1/MU2=P1/P2 dTU3?88ÆäÖУ¬ÓÉÒÔÖªµÄЧÓú¯ÊýU?xx ¿ÉµÃ£ºMU1??x1x2 dx18dTU58?8 MU2??x1x2 dx283?88x1x23x2PP18?1 ?ÓÚÊÇ£¬ÓУºÕûÀíµÃ£º335x1P258?8P2x1x28¼´ÓÐx2?5535881255335p1x1 £¨1£© 3p2P1x1?P25P1x1?M3M5M3P2½âµÃ£ºx1?´úÈ루1£©Ê½µÃ x2? 8P18P2£¨1£©Ê½´úÈëÔ¼ÊøÌõ¼þP1X1+P2X2=M£¬ÓУº ËùÒÔ£¬¸ÃÏû·ÑÕß¹ØÓÚÁ½ÉÌÆ·µÄÐèÇóº¯ÊýΪx1?3M5M x2? 8P18P28. ½â´ð£ºÓÉÓÚÎÞ²îÒìÇúÏßÊÇÒ»ÌõÖ±Ïߣ¬ËùÒÔ¸ÃÏû·ÑÕßµÄ×îÓÅÏû·ÑÑ¡ÔñÓÐÈýÖÖÇé¿ö£¬ÆäÖеĵÚÒ»¡¢µÚ¶þ ÖÖÇé¿öÊôÓڱ߽ǽ⡣ µÚÒ»ÖÖÇé¿ö£ºµ±MRS12>P1/P2ʱ£¬¼´a> P1/P2ʱ£¬Èçͼ£¬Ð§ÓÃ×î´óµÄ¾ùºâµãEµÄλÖ÷¢ÉúÔÚºáÖᣬËü±íʾ´ËʱµÄ×îÓŽâÊÇÒ»¸ö±ß½Ç½â£¬¼´ X1=M/P1£¬X2=0¡£Ò²¾ÍÊÇ˵£¬Ïû·ÑÕß½«È«²¿µÄÊÕÈë¶¼¹ºÂòÉÌÆ·1£¬²¢ÓÉ´Ë´ïµ½×î´óµÄЧÓÃˮƽ£¬¸ÃЧÓÃˮƽÔÚͼÖÐÒÔʵÏß±íʾµÄÎÞ²îÒìÇúÏß±ê³ö¡£ÏÔÈ»£¬¸ÃЧÓÃˮƽ¸ßÓÚÔڼȶ¨µÄÔ¤ËãÏß 12