作业帮关于定积分的应用题.
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/18 03:25:46
关于定积分的应用题.
P² = k/x
当x = 100时P = 50
50² = k/100 ==> k = 250000
P² = 250000/x ==> P = 500/√x
c(x) = 1200 + 2x³/75
设利润为R
R = Px - c(x)
= 500/√x • x - (1200 + 2x³/75)
= 500√x - 1200 - 2x³/75
R' = 250/√x - 2x²/25
R'' = - 125/x^(3/2) - 4x/25
令R' = 0
250/√x - 2x²/25 = 0
x = 25
R''(25) = - 5 < 0,取得极大值
所以产量为为25件时总利润有R(25) = 2650/3,为最大.
当x = 100时P = 50
50² = k/100 ==> k = 250000
P² = 250000/x ==> P = 500/√x
c(x) = 1200 + 2x³/75
设利润为R
R = Px - c(x)
= 500/√x • x - (1200 + 2x³/75)
= 500√x - 1200 - 2x³/75
R' = 250/√x - 2x²/25
R'' = - 125/x^(3/2) - 4x/25
令R' = 0
250/√x - 2x²/25 = 0
x = 25
R''(25) = - 5 < 0,取得极大值
所以产量为为25件时总利润有R(25) = 2650/3,为最大.