Question

The point at which a company's profits equal zero is called the company's break-even point. let R represent a company's revenue, let C represent the company's costs, and let x represent the number of units produced and sold each day.
R(x)=12x
C(x)=6.5x+22000
a) Find the firm's break-even point; that is, find x so that R=C
b) Find the values of x such that R(x)>C(x). this represents the number of units that the company must sell to earn a profit.

Answer 1

a)     R=C implies 12x=6.5x + 22000, and then 12x - 6.5x= 22000, 5.5x= 22000, from where we find x = 22000 : 5.5,     x=4000.

b)     For R(x)>C(x), we get 12x>6.5x + 22000, which implies after the same calculation,  x>4000

Answer 2

R ( x ) = 12 x ( revenue )
C ( x ) = 6.5 x + 22,000 ( cost )
a ) Break-even point : R ( x ) = C ( x )
12 x = 6.5 x + 22,000
12 x - 6.5 x = 22,000
5.5 x = 22,000
x = 22,000 : 5.5
x = 4,000
b ) R ( x ) > C ( x ) 
x > 4,000
The number of units that the company must sell to earn a profit is 4,001 or more.