Question

7£®Ä³¹«Ë¾Éú²úµÄijÖÖʱÁîÉÌƷÿ¼þ³É±¾Îª20Ôª£¬¾­¹ýÊг¡µ÷Ñз¢ÏÖ£¬ÕâÖÖÉÌÆ·ÔÚδÀ´40ÌìÄÚµÄÈÕÏúÊÛÁ¿m£¨¼þ£©Óëʱ¼ät£¨Ì죩µÄ¹ØϵÈçÏÂ±í£º

ʱ¼ät/Ìì	1	3	6	10	36	¡­
ÈÕÏúÊÛÁ¿m/¼þ	94	90	84	76	24	¡­

δÀ´40ÌìÄÚ£¬Ç°20ÌìÿÌìµÄ¼Û¸ñy₁ £¨Ôª/¼þ£©Óëʱ¼ät£¨Ì죩µÄº¯Êý¹ØϵʽΪy₁=0.25t+25£¨1¡Üt¡Ü20ÇÒtΪÕûÊý£©£¬ºó20ÌìÿÌìµÄ¼Û¸ñy₂ £¨Ôª/¼þ£©Óëʱ¼ät£¨Ì죩µÄº¯Êý¹Øϵʽy₂=-0.5+40£¨21¡Üt¡Ü40ÇÒtΪÕûÊý£©£®
ÏÂÃæÎÒÃǾÍÀ´Ñо¿ÏúÊÛÕâÖÖÉÌÆ·µÄÓйØÎÊÌ⣺
£¨1£©ÈÏÕæ·ÖÎöÉϱíÖеÄÊý¾Ý£¬ÓÃËùѧ¹ýµÄÒ»´Îº¯Êý¡¢¶þ´Îº¯Êý¡¢·´±ÈÀýº¯ÊýµÄ֪ʶȷ¶¨Ò»¸öÂú×ãÕâЩÊý¾ÝµÄm£¨¼þ£©Óët£¨Ì죩֮¼äµÄ¹Øϵʽ£»
£¨2£©ÇëÔ¤²âδÀ´40ÌìÖÐÄÄÒ»ÌìµÄÈÕÏúÊÛÀûÈó×î´ó£¬×î´óÈÕÏúÊÛÀûÈóÊǶàÉÙ£¿
£¨3£©ÔÚʵ¼ÊÏúÊÛµÄÇ°20ÌìÖУ¬¸Ã¹«Ë¾¾ö¶¨Ã¿ÏúÊÛÒ»¼þÉÌÆ·£¬¾Í¾èÔùaÔªÀûÈó£¨a£¼4£©¸øÏ£Íû¹¤³Ì£®¹«Ë¾Í¨¹ýÏúÊۼǼ·¢ÏÖ£¬Ç°20ÌìÖУ¬Ã¿Ìì¿Û³ý¾èÔùºóµÄÈÕÏúÊÛÀûÈóËæʱ¼ät£¨Ì죩µÄÔö´ó¶øÔö´ó£¬ÇëÖ±½Óд³öaµÄÈ¡Öµ·¶Î§£®

Answer 1

·ÖÎö £¨1£©´Ó±í¸ñ¿É¿´³öÿÌì±ÈÇ°Ò»ÌìÉÙÏúÊÛ2¼þ£¬ËùÒÔÅжÏΪһ´Îº¯Êý¹Øϵʽ£»
£¨2£©ÈÕÀûÈó=ÈÕÏúÊÛÁ¿¡Áÿ¼þÀûÈ󣬾ݴ˷ֱð±íʾǰ20ÌìºÍºó20ÌìµÄÈÕÀûÈ󣬸ù¾Ýº¯ÊýÐÔÖÊÇó×î´óÖµºó±È½ÏµÃ½áÂÛ£»
£¨3£©ÁÐʽ±íʾǰ20ÌìÖÐÿÌì¿Û³ý¾èÔùºóµÄÈÕÏúÊÛÀûÈ󣬸ù¾Ýº¯ÊýÐÔÖÊÇóaµÄÈ¡Öµ·¶Î§£®

½â´ð ½â£º£¨1£©ÓÉÌâÒâ¿ÉÖª£¬m£¨¼þ£©Óët£¨Ì죩Âú×ãÒ»´Îº¯Êý¹Øϵ£®
ÉèÒ»´Îº¯Êý¹ØϵʽΪm=kx+b£¬½«$\left\{\begin{array}{l}{t=1}\\{m=94}\end{array}\right.$ºÍ$\left\{\begin{array}{l}{t=3}\\{m=90}\end{array}\right.$·Ö±ð´úÈëÒ»´Îº¯Êý¹Øϵʽm=kx+bÖУ¬
µÃ$\left\{\begin{array}{l}{94=k+b}\\{90=3k+b}\end{array}\right.$£¬
½âµÃ$\left\{\begin{array}{l}{k=-2}\\{b=96}\end{array}\right.$£¬
¡àm=-2t+96£¬
¾­¼ìÑ飬ÆäËûmÓëtµÄ¶ÔÓ¦Öµ¾ùÊʺÏÒÔÉϹØϵʽ£¬¹ÊËùÇó¹ØϵʽΪm=-2t+96£®

£¨2£©ÉèÇ°20ÌìÈÕÏúÊÛÀûÈóΪP₁Ôª£¬ºó20ÌìÈÕÏúÊÛÀûÈóΪP₂Ôª£¬
ÔòP₁=£¨-2t+96£©£¨0.25t+25-20£©£¬
=-$\frac{1}{2}$t²+14t+480£¬
=-$\frac{1}{2}$£¨t-14£©²+578£®
¡ß1¡Üt¡Ü20£¬
¡àµ±t=14ʱ£¬P₁ÓÐ×î´óÖµ£¬Îª578£®
P₂=£¨-2t+96£©£¨-0.5t+40-20£©£¬
=t2-88t+1920=£¨t-44£©²-16£¬
¡ß21¡Üt¡Ü40£¬´Ëº¯ÊýͼÏóµÄ¶Ô³ÆÖáÊÇÖ±Ïßt=44£¬
¡àµ±t=21ʱ£¬P₂ÓÐ×î´óÖµ£¬Îª£¨21-44£©²-16=513£®
¡ß578£¾513£¬
¡àµÚ14ÌìµÄÈÕÏúÊÛÀûÈó×î´ó£¬Îª578Ôª£®

£¨3£©ÓÉÌâÒâµÃ£ºP=£¨-2t+96£©£¨$\frac{1}{4}$t+5-a£©£¨1¡Üt¡Ü20£©
Åä·½µÃ£ºP=-$\frac{1}{4}$[t-2£¨a+7£©]²+2£¨a-17£©²£¨1¡Üt¡Ü20£©£¬
ҪʹÈÕÏúÊÛÀûÈóËæʱ¼ätÔö´ó¶øÔö´ó£¬ÔòÒªÇó¶Ô³ÆÖáx=2£¨a+7£©¡Ý20½âµÃa¡Ý3£»
ÓÖÌâÄ¿ÒªÇóa£¼4£¬¹Ê3¡Üa£¼4£®

µãÆÀ ´ËÌâÖ÷Òª¿¼²éÁ˶þ´Îº¯ÊýµÄÓ¦Óã¬ÊìÁ·ÕÆÎÕ¸÷º¯ÊýµÄÐÔÖʺÍͼÏóÌØÕ÷£¬Õë¶ÔËù¸øÌõ¼þ×÷³ö³õ²½ÅжϺóÐèÑéÖ¤ÆäÕýÈ·ÐÔ£¬×îÖµÎÊÌâÐèÓɺ¯ÊýµÄÐÔÖÊÇó½âʱ£¬ÕýÈ·±í´ï¹ØϵʽÊǹؼü£®