You are given a price-demand function,
p(x) = −1.2x + 70,
where x is the number of items made and sold and
p(x)
is the price per item (in dollars). Write the revenue function,
R(x),
(in dollars) for the sale of x items.
R(x) =


Use the revenue function,
R(x) = −8x2 + 176x,
and cost function,
C(x) = 80x + 160,
where x is the number of items made and sold, to determine each of the following. Assume both revenue and cost are given in dollars. Enter multiple answers using a comma-separated list when necessary.
(a)
Find the number of items sold when revenue is maximized.
items
(b)
Find the maximum revenue (in dollars).
$
(c)
Find the number of items sold when profit is maximized.
items
(d)
Find the maximum profit (in dollars).
$
(e)
Find the break-even quantity/quantities. (Enter your answers as a comma-separated list.

State the real zeros of
p(x) = (7x + 6)4(4x + 5)(x + 7)2x4.
Give exact and reduced answers as a comma-separated list. If the polynomial has no real zeros, type DNE.
x =
3.) For
f(x) = 5x2 + 40x + 79,
determine the following without the use of technology, if they exist. If something does not exist, enter DNE. Use a comma-separated list to enter multiple answers when necessary.
(a)
vertex
(x, y) =
(b)
axis of symmetry
(c)
domain (Enter your answer using interval notation.
(d)
range (Enter your answer using interval notation.)
(e)
x-intercept(s) (Enter the x-intercepts as exact numbers, using radicals.)
smaller x-value
(x, y)
=
larger x-value
(x, y)
=
(f)
y-intercept
(x, y) =
(g)
maximum
(h)
minimum value


Drives Co. sells portable hard drives. They can sell 600 drives when the price is $75/drive, and they can sell 720 drives when the price is $45/drive.
If x represents the number of drives sold, determine the following.
(a)
What is Drive Co.'s revenue function?
R(x) =
What is the price per drive (in dollars) when revenue is maximized?
$
(c)
What is the maximum profit (in dollars) made from the sale of these drives if Drive Co. incurs production costs of $175 per drive and has fixed costs of $665?