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.)

Question

Mathematics

Elise Adams

23 October, 16:02

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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Answers (1)

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Jaidyn Dunlap · Answer 1

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