某种汽车:(A)购买时费用为10万元.(B)每年应交保险费、养路费及汽油

某种汽车:(A)购买时费用为10万元.(B)每年应交保险费、养路费及汽油费合计为9千元.(C)汽车的维修费为:第一年2千元,第二年4千元,第三年6千元,这样依等差数列逐年递增.问这种汽车使用多少年报废最合理(即使用多少年平均费用最少)?

答案

解:Sn=10+0.9n+(0.2+0.4+…+0.2n)=0.1n2+n+10,

∴平均费用为=0.1n++1≥2.

当0.1n=,即n=10时,最少.

故使用10年报废最合理.

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