问题 解答题
某投资公司投资甲乙两个项目所获得的利润分别是M(亿元)和N(亿元),它们与投资额t(亿元)的关系有经验公式:M=
1
3
t
,N=
1
6
t
,今该公司将3亿元投资这个项目,若设甲项目投资x亿元,投资这两个项目所获得的总利润为y亿元.
(1)写出y关于x的函数表达式;
(2)求总利润y的最大值.
答案

(1)设甲项目投资x亿元,则乙项目投资(3-x)亿元,这两个项目所获得的总利润为:

y=

1
3
x
+
1
6
(3-x),x∈[0,3];

(2)设

x
=t,t∈[0.
3
]
,则x=t2

y=

1
3
t+
1
6
(3-t2)=
1
6
[-(t-1)2+4]

∵t∈[0,

3
],

∴当t=1,即x=1时,y有最大值为

2
3

答:总利润的最大值是

2
3
亿元

单项选择题
改错题
单句改错。
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