Question

A small company of science writers found that its rate of profit (in thousands of dollars) after t years of operation is given by ? ′ (?) = (? + 3)(? 2 + 6? + 3) 1/3 . Find the total profit in the first three years of operation (round your answer to the nearest thousandth).

Answer #1

A small company of science writers found that its rate of profit
(in thousands of dollars) after t years of operations is given by
the function below
p'(t)=(6t+6)(t^2+2t+2)^1/3
A. find the total profit in the first three years
B. find the profit in the fourth year of operations.
c. what is happening to the annual profit over the long run

The profit P (in thousands of dollars) for a company
spending an amount s (in thousands of dollars) on
advertising is shown below.
P = −1/3 s3 + 9s2 + 400
(a) Find the amount of money the company should spend on
advertising in order to yield a maximum profit.
s = thousands of dollars (b) The
point of diminishing returns is the point at which the
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The profit P (in thousands of dollars) for a company spending an
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maximum profit. Also, Find the point of diminishing returns.

Suppose the Sunglasses Hut Company has a profit function given
by P(q)=-0.01q2+4q-26, where q is the number of thousands of pairs
of sunglasses sold and produced, and P(q) is the total profit, in
thousands of dollars, from selling and producing q pairs of
sunglasses.
A) Find a simplified expression for the marginal profit function.
(Be sure to use the proper variable in your answer.)
Answer: MP(q)=
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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)=130et, R(0)=0; C′(t)=130−0.8t, C(0)=0
a) Find the total profit P(T) from
t=0 to t=10
(the first 10 days).
P(T)=R(T)−C(T)=∫T0R′(t)−C′(t) dt
The total profit is $___
(Round to the nearest cent...

A construction company has an expenditure rate of E(x) = e^0.12x
dollars per day on a particular paving job and an income rate of
I(x) = 115.7 - e^0.12x dollars per day on the same job, where x is
the number of days from the start of the job. The company's profit
on that job will equal total income less total expenditures. Profit
will be maximized if the job ends at the optimum time, which is the
point where the...

Suppose that a printing firm considers its production as a
continuous income stream. If the annual rate of flow at time
t is given by
f(t) =
91.5e−0.8(t + 3)
in thousands of dollars per year, and if money is worth 8%
compounded continuously, find the present value and future value
(in dollars) of the presses over the next 10 years. (Round your
answers to the nearest dollar.)
present value$ =
future value$ =

(1 point) This problem is similar to one in your textbook.
Suppose that a company needs new equipment, and that the machinery
in question earns the company revenue at a continuous rate of
58000t+42000 dollars per year during the first six months of
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a) Find the present value of...

A one-product company finds that its profit, P, in millions
of dollars, is given by the following equation where a is the
amount spent on advertising, in millions of dollars, and p is the
price charged per item of the product, in dollars.
P(a,p)=4 ap + 50 p - 9 p^2 - one tenth a^2 p - 90
Find the maximum value of P and the values of a and p at which
it is attained. The maximum value...

The table shows the total 4-year cost (in thousands of dollars)
and the Graduation rate (nearest percentage) from 4 randomly
selected colleges/universities in the U.S. Cost, x 129 104 88 69
Graduation Rate, y 45 62 30 35 The mean of x is 97.5 The standard
deviation of x is 25.410 The mean of y is 43 The standard deviation
of y is 14.119 The deviations and the z-scores for each x and y
value are given below: (x -...

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