Math, asked by annyeonghaseyo02, 6 hours ago

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

Answers

Answered by satyamdaga01
1

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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