Finding break-even point with information given in problem

Question

A division of the Gibson Corporation manufactures bicycle pumps. Each pump sells for $9, and the variable cost of producing each unit is 20% of the selling price. The monthly fixed costs incurred by the division are $50,000. What is the break-even point for the division? (Round your answers to the nearest whole number.)

Answer 1

Let x = number of pumps sold

 

Revenue = (price)(quantity) = 9x

 

Cost = fixed cost + variable costs = 50000 + 0.20(9x)

                                                          = 50000 + 1.8x

 

The company breaks even when revenue = cost

 

9x = 50000 + 1.8x

 

7.2x = 50000

 

x = 6944.444 ≈ 6944 bicycle pumps