The total cost of production consists of fixed costs such as

The total cost of production consists of fixed costs (such as overhead) plus variable costs (such as supplies). Revenue is the amount of money that is received due to sales. Suppose that the 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 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. The company will break even (no profit and no loss) as long as revenue just equals cost. The value of x (the number of items produced and sold) where C(x) = R(x) is called the break-even point.

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? Is the manager better off in this case or not?

Solution

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

C(x) = 1000 + 200*x

Each unit of tile sells for $240

R(x) = 240*x

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

1000 + 200x = 240x

40x = 1000 ; x= 25 units

At breakeven , C(x) = R(x) = 1000 +200*40 = 1000 + 8000 = $ 9000

If varible cost = $ 220

C(x) = 1000 + 200*x

C(x) = 1000 + 220*x

Breakeven: 1000 + 220x = 240x

x = 1000/20 = 50 units

At breakeven C(50) = 1000 +220*50 = $ 12000