An Oil Company's revenue rate (in millions of dollars per year)
at time t years is given by
R'(t) = 9 −√t
and the corresponding cost rate function (in millions of dollars)
is given by
C'(t) =1 + 3√t
Determine how long the oil company should continue to operate
and what the total profit will be at the end of the option.
Hint: Profit is maximum when marginal revenue equals marginal cost
please maths experts help asap
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Answer:
it should continue till C'(t) < R'(t)
1 + 9t + 6√t = 81 + t - 18√t
8t - 80 = - 24√t
t -10 = -3√t
t^2 +100 - 20t = 9t
t^2 -29 t + 100 = 0
t= 4 or 25
so the oil company should run till t = 4
profit can be counted by integrating both from 0 to 4 and subtracting total profit - cost
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