The marginal cost and marginal revenue of a mining operation are
C'(t)=3(1+t^(1/2)), R'(t)=19-t^(1/2),
where t is the number of years from now and C and R are measures in millions of dollars. Determine how long the operation should continue in order to maximize the profit and find the maimun profit that can be generates during this period.
T H X !!!
唔識唔識IN--LQ
2008-06-16 12:02 am
回答 (1)
2008-06-17 10:45 pm
✔ 最佳答案
OKBy economics, if dR/dt＞ dC/dt, then the operation should continue (because you earn money)
So when dR/dt= dC/dt,the operation will stop
3(1+t^(1/2))=19-t^(1/2)
4t^(1/2) = 16
t^(1/2) = 4
t=16
Now C(t)=3(t+(2/3)t^(3/2)),R(t)=19t-(2/3)t^(3/2)
C(16)=176
R(16)=261.33
the maimun profit that can be generates during this period
=216.33-176
=85.33
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