Find the total cost in dollars, C(x), of producing x units of tile and the revenue in dollars, R(x), from the sale of x units of tile.

Question

manager of a small company that produces roof tile has determined that the overhead is $1000 and the variable cost for each unit of tile produced is $200. Each unit of tile sells for $240. 

 

Find the break-even point and the cost and revenue at the break-even point. Suppose the variable cost is actually $220 per unit, instead of $200.

 

How does this affect the break-even point?

Answer 1

Find the total cost in dollars, C(x), of producing x units of tile and the revenue in dollars, R(x), from the sale of x units of tile.
manager of a small company that produces roof tile has determined that the overhead is $1000 and the variable cost for each unit of tile produced is $200.
Each unit of tile sells for $240.

Find the break-even point and the cost and revenue at the break-even point. Suppose the variable cost is actually $220 per unit, instead of $200.

How does this affect the break-even point?

R(x) = 240x
C(x) = 1000 + 200x

Break-even R(x) = C(x)

240x = 1000 + 200x
40x = 1000
x = 25
R(25) = C(25) = 6000

if variable cost is 220 per unit

C(x) = 1000 + 220x
R(x) = C(x) = 240x = 1000 + 220x


20x = 1000
x = 50

break-even point is 50 units instead of 25 units