A musician is planning to market a CD. The fixed costs are $840 and the variable costs are $6 per CD. The wholesale price of the CD will be $10. For the artist to make a profit, revenues must be greater than costs.
How many CDs, x, must be sold for the musician to make a profit?

Question

A musician is planning to market a CD. The fixed costs are $840 and the variable costs are $6 per CD. The wholesale price of the CD will be $10. For the artist to make a profit, revenues must be greater than costs.
How many CDs, x, must be sold for the musician to make a profit?

cruffo · Answer

C(x) = 840+6x
R(x) = 10x
P(x) = R(x) - C(x)
      = 10x - (840+6x)
      = 10x - 840 - 6x
      = 4x - 840
To finish, set the above = 0 and solve for x.  This value of x is called the "break-even" point.  Since P(x) is a line with positive slope, and value of x greater than the value you find is when the artist makes a (positive) profit.