The monthly demand function for x units of a product sold by a monopoly is p = 6,400 −1/2x2 dollars, and its average cos

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The monthly demand function for x units of a
product sold by a monopoly
is p = 6,400 −1/2x2 dollars, and
its average cost is C = 3,020 +
2x dollars. Production is limited
to 100 units.
Find the revenue function,
R(x),
in dollars.
A large corporation with monopolistic control in the marketplace
has its average daily costs, in dollars, given by
C =
+ 100x + x2.
The daily demand for x units of its product
is given by
p = 360,000 − 50x dollars.
Find the quantity that gives maximum profit.
x = units

Find the maximum profit.
$

What selling price should the corporation set for its
product?
$
R(x) =
Find the cost function,
C(x),
in dollars.
C(x) =
Find the profit function,
P(x),
in dollars.
P(x) =
Find
P'(x).
P'(x) =
Find the number of units that maximizes profits. (Round your
answer to the nearest whole number.)
units
Find the maximum profit. (Round your answer to the nearest
cent.)
$
Does the maximum profit result in a profit or loss?