# [SOLVED] Revenue Equation help

• Feb 10th 2008, 08:21 PM
Space Comet
[SOLVED] Revenue Equation help

The profit p (in thousands of dollars) on x thousand units of a specialty item is p = 0.8x - 15.5. The cost c of manufacturing x items is given by c = 0.6x + 15.5 .

Find an equation that gives the revenue r from selling x items.

How many items must be sold for the company to break even (i.e., for revenue to equal cost)?

Round to the nearest integer.
• Feb 10th 2008, 08:48 PM
topher0805
Profit is revenue minus the cost, so:

\$\displaystyle p = r - c\$

Therefore, to find the revenue we have:

\$\displaystyle r = p + c\$

So we add the two equations:

\$\displaystyle
(0.8x - 15.5) + (0.6x + 15.5)
\$

To get:

\$\displaystyle 1.4x\$

Therefore, \$\displaystyle r = 1.4x\$

To find when you will break even, simply set the two equations equal to each other:

\$\displaystyle 1.4x = 0.6x + 15.5\$

To get:

\$\displaystyle 0.8x = 15.5\$

Therefore, \$\displaystyle x = 19.375\$

Note that another way of finding when you will break even is to set the profit equal to 0:

\$\displaystyle 0.8x - 15.5 = 0\$

Which gives you the same result:

\$\displaystyle
x = 19.375\$