【題目】要建造一個容積為1 600立方米，深為4米的長方體無蓋蓄水池，池壁的造價為每平方米200元，池底的造價為每平方米100元．
（1）把總造價y元表示為池底的一邊長x米的函數；
（2）由于場地原因，蓄水池的一邊長不能超過20米，問蓄水池的這個底邊長為多少時總造價最低？總造價最低是多少？
【答案】（1）y＝1 600（x＋
）＋40 000，x∈（0，＋∞）；（2）20，104 000
【解析】（1）由已知得池底的面積為
＝400（平方米），底面的另一邊長為
米，則池壁的面積為2×4×（x＋
）平方米．
所以y＝1 600（x＋
）＋40 000，x∈（0，＋∞）．
（2）由（1）知y＝1 600（x＋
）＋40 000（0＜x≤20），
設0＜x1＜x2≤20，則
y1－y2＝1 600（x1＋
）－1 600（x2＋
）
＝1 600[（x1－x2）＋
]
＝1 600（x1－x2）（1－
）．
∵0＜x1＜x2≤20，∴x1－x2＜0，1－
＜0，得y1－y2＞0，即y1＞y2.
從而這個函數在（0，20]上是減函數，故當x＝20時，ymin＝10 4000.
所以當池底是邊長為20米的正方形時，總造價最低，為104 000元．
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