【題目】某人上午時(shí)， 乘摩托艇以勻速從港出發(fā)到距的港去， 然后乘汽車以勻速自港向距的市駛?cè)ィ畱?yīng)該在同一天下午至點(diǎn)到達(dá)市． 設(shè)乘坐汽車、 摩托艇去目的地所需要的時(shí)間分別是.

（1）作圖表示滿足上述條件的范圍；

（2）如果已知所需的經(jīng)費(fèi)（元），那么分別是多少時(shí)最小？ 此時(shí)需花費(fèi)多少元？

【答案】（1）；（2）的最小值為元．

【解析】

試題分析：（1）依題意得 解出所滿足的范圍，作出符合條件的圖形；（2）先確定目標(biāo)函數(shù)，由題意得得出，由（1）中圖可知，當(dāng)先經(jīng)過(guò)點(diǎn)時(shí)，目標(biāo)函數(shù)取得最小值，即可求解結(jié)論.

試題解析：（1）依題意得

①

由于乘汽車、摩托艇所需的時(shí)間和應(yīng)在至 個(gè)小時(shí)之間，即 ②

因此，滿足①②的點(diǎn)的存在范圍是圖中陰影部分（包括邊界）

（2），上式表示斜率為的直線，

當(dāng)動(dòng)直線通過(guò)圖中的陰影部分區(qū)域（包括邊界），通過(guò)點(diǎn)時(shí)，值最小．

由得，即當(dāng)時(shí)，最小．

此時(shí)，的最小值為 元．

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