## A company determines that its marginal revenue per day is given by R’ ( t ) , where R ( t ) is the total accumulated revenue, in dollars, on

Question

A company determines that its marginal revenue per day is given by R’ ( t ) , where R ( t ) is the total accumulated revenue, in dollars, on the tth day. The company’s marginal cost per day is given by C’ ( t ) , where C ( t ) is the total accumulated cost, in dollars, on the tth day. R’ ( t ) = 80 e t, R ( 0 ) = 0; C’ ( t ) = 80 – 0.8t, C ( 0 ) = 0 Find the total profit P ( T ) from t = 0 to t = 10 ( the first 10 days ) . P ( T ) = R ( T ) – C ( T ) = [R’ ( t ) – C’ ( t ) ] dt The total profit is \$ . ( Round to the nearest cent as needed. ) Find the average daily profit for the first 10 days. The average daily profit is \$ . ( Round to the nearest cent as needed. )

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1 week 2021-09-15T01:31:10+00:00 1 Answer 0

Step-by-step explanation:

Total profit function is equal to Total revenue function minus Total Cost function.

To get both Revenue function and Cost function, integrate the Marginal functions as follows:

R(t) = 108.7312t^2

Where 80et = 217.4624t

(e =2.71828)

C(t) = 80t – 0.4t^2

P(t) = R(t) – C(t) = 109.1312t^2 – 80t

When t=0, P=0

When t=1, P=29.1312

When t=2, P=276.5248

When t=3, P=742.1808

And so on …

Summing the daily profits, total profit for the 10 days is 37,615.512 dollars which equals 3,761551.2 cents

(B)

Average daily profit for the first 10 days (in dollars) is 37,615.512÷10 = 3,761.5512 dollars

= 376,155.12 cents