How many cabinets must he sell to break even?

Question

john thunderhawk is making furniture. he finds that to design a particular cabinet and set up his shop to produce it costs $1,400. Then the labor and supplies to build each one are $400. so his cost, y, for x items is represented by y=1,400/400x. He can sell the cabinets for $600. So his revenue, y, is represented by y=600x. The solution to this system of equations is his break-even point, the point beyond which he starts making a profit. How many cabinets must he sell to break even?

Answer 1

If x = number of cabinets produced

y = cost to produce the cabinets

Your cost equation is:

y = 1400 + 400x     because the $1400 is a one time only cost

 

Revenue = 600x

r = 600x

 

To break even the cost must be equal to the revenue

 

600x = 1400 + 400x

subtract 400x from both sides

200x = 1400

divide both sides by 200

x = 1400/200

x = 7

 

To break even he must sell produce and sell 7 cabinets