A company has found that when x units of a product are manufactured and sold,its revenue is given by x 2 + 100 x dollars and its costs are given by...

Let the revenue be R, the profit be P, and the cost be
C.

Then, we know that:

Profit
= Revenue - cost

==> Given that R=
x^2+100x

Also, given that C =
240x+500

==> P = x^2 +100x - 240x
-500

==> P = x^2 -140x
-500

We need to find x such that P=
10,000

==> x^2 - 140x -500 =
10,000

==> x^2 -140x -10,500 =
0

We will use the formula to find the
roots.

==> x1= ( 140+248.2)/2 = 194.1 (
approx.)

Then, the number of product must be
sold is 194.