Question

The point at which a company's costs equal its revenues is the break-even point. C represents the cost, in dollars, of x units of a product and R represents the revenue, in dollars, from the sale of x units. Find the number of units that must be produced and sold in order to break even. That is, find the value of x for which C=R.

C=13x+80 and R=18x.
How many units must be produced and sold in order to break even?

Answer 1

This is the concept of financial mathematics;
Break even point is defined mathematically as:
Cost=Revenue
At this point the organization doesn't make any profits because the cost is equal to the revenue. Therefore , to solve our expression we proceed as follows;
The question requires us to find the number of units of products that must be sold in order to break even, to solve this we proceed as follows;
At break even;
C=R
but;
C=13x+80
R=18x
hence;
18x=13x+80
putting the like terms together we get:
18x-13x=80
5x=80
dividing both sides by 5 we get:
(5x)/5=80/5
x=16
Therefore the number of units that must be sold in order to break even is:
x=16 units