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arianaguerin
06.12.2019 •
Mathematics
Acompany 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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Ответ:
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
Ответ:
The answer is 31.4
Step-by-step explanation: