1. [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.

2. 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:

$\displaystyle x = 19.375$