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    【题目】某人上午时， 乘摩托艇以匀速从港出发到距的港去， 然后乘汽车以匀速自港向距的市驶去．应该在同一天下午至点到达市． 设乘坐汽车、 摩托艇去目的地所需要的时间分别是.

    （1）作图表示满足上述条件的范围；

    （2）如果已知所需的经费（元），那么分别是多少时最小？ 此时需花费多少元？

    【答案】（1）；（2）的最小值为元．

    【解析】

    试题分析：（1）依题意得 解出所满足的范围，作出符合条件的图形；（2）先确定目标函数，由题意得得出，由（1）中图可知，当先经过点时，目标函数取得最小值，即可求解结论.

    试题解析：（1）依题意得

    ①

    由于乘汽车、摩托艇所需的时间和应在至 个小时之间，即 ②

    因此，满足①②的点的存在范围是图中阴影部分（包括边界）

    （2），上式表示斜率为的直线，

    当动直线通过图中的阴影部分区域（包括边界），通过点时，值最小．

    由得，即当时，最小．

    此时，的最小值为 元．

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