题目
已知某种水果的批发单价与批发量的函数关系如图(1)所示. (1). 请说明图中①、②两段函数图象的实际意义; (2). 写出批发该种水果的资金金额w(元)与批发量n(kg)之间的函数关系式;在下图的坐标系中画出该函数图象;指出金额在什么范围内,以同样的资金可以批发到较多数量的该种水果.3经调查,某经销商销售该种水果的日最高销量与零售价之间的函数关系如图(2)所示,该经销商拟每日售出60kg以上该种水果,且当日零售价不变,请你帮助该经销商设计进货和销售的方案,使得当日获得的利润最大.
答案: 解:图①表示批发量不少于20kg且不多于60kg的该种水果,可按5元/kg批发; 图②表示批发量高于60kg的该种水果,可按4元/kg批发.…………………2分2解:由题意得:图象如图所示.…………5分由图可知,资金金额满足时,以同样的资金可批发到较多数量的该种水果.·············6分(3).解法一:设当日零售价为x元,由图可得日最高销量当n>60时,x<6.5.由题意,销售利润为······································8分从而x=6时,.此时n=80.即经销商应批发80kg该种水果,日零售价定为6元/kg,当日可得最大利润160元.··························································································10分解法二:设日最高销量为xkg(x>60)则由图(2)日零售价p满足:.于是,销售利润··························· 8分从而x=80时,.此时p=6.即经销商应批发80kg该种水果,日零售价定为6元/kg,当日可得最大利润160元.····························································································································10分解析:略