VCE低数（FM）干货帖之Break-even analysis

Break-even analysis (收支平衡分析)

The aim of most businesses is to make a profit. The profit depends on the costs associated with

the business (labour, raw materials and plant) and its revenue (the money it earns through

sales). It represents the difference between the revenue and the costs.

Cost: the expenses a company pays

Revenue: the money the company receives

At the break-even point （收支平衡点）:

Profit（利润） = Revenue（收益）- Costs（支出）

Revenue（收益）= Costs（支出）

Example

A firm sells its product at $20 per unit. The cost of production is given by the rule

C=4x+4800

Where x is the number of units produced

a) Find the number of units that must be produced for the firm to break even

b) Find the profit when the company manufactures:

i. 200 units

ii. 400 units

iii. 1000units

Answer：

a) R=20x, where x is the number of units sold

C=4x+4800

20x=4x+4800

X=300

b) P=R-C=20x-(4x+4800)=16x-4800

i. P(200)=-$1600

ii. P(400)=$1600

iii. P(1000)=$11200