【題目】小王在年初用50萬元購買一輛大貨車，第一年因繳納各種費用支出6萬元，從第二年起，每年都比上一年增加支出2萬元，假定該車每年的運輸收入均為25萬元.小王在該車運輸累計收入超過總支出后，考慮大貨車作為二手車出售，若該車在第年年底出售，其銷售價格為25-萬元（國家規(guī)定大貨車的報廢年限為10年）.

（1）大貨車運輸?shù)降趲啄昴甑祝撥囘\輸累計收入超過總支出？

（2）在第幾年年底將大貨車出售，能使小王獲得的年平均利潤最大（利潤=累計收入+銷售收入-總支出）？

【答案】(1)；(2)．

【解析】

試題分析：(1)設(shè)大貨車運輸?shù)降?/span>年年底，該車運輸累計收入與總支出的差為元，則（，），令進而得出即可得到結(jié)論；(2)由利潤累計收入銷售收入總支出，得出年平均利潤為，即可利用基本不等式求解最值，得出結(jié)論.

試題解析：（1）設(shè)大貨車運輸?shù)降?/span>年年底，該車運輸累計收入與總支出的差為元，則（，）

由，可得

∵，故從第三年，該車運輸累計收入超過總支持；

（2）∵利潤=累計收入+銷售收入-總支出，

∴二手車出售后，小王的年平均利潤為

當(dāng)且僅當(dāng)時，等號成立.

∴小王應(yīng)當(dāng)在第5年將大貨車出售，能使小王獲得的年平均利潤最大.

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