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Break-Even Analysis

Break-even occurs when total income equals total expenses.

$$Total\ Revenue=Total\ Cost$$

Problem 95: CE Board Nov. 2015

A new computer desk requires $6,000 equipment cost and $200 construction cost per desk. Revenue is $450 per desk. Find the break-even quantity.

$$200x+6000=450x$$
$$x=24$$

Final answer: 24 desks.

Problem 97: CE Board Nov. 2018

Revenue from selling computer boards is $R=60x$ and cost is $C=50x+5000$. Find the break-even number of boards and production cost at break-even.

$$60x=50x+5000 \Rightarrow x=500$$
$$C=50(500)+5000=30,000$$

Final answer: 500 boards and $30,000 cost.

Problem 99: CE Board Nov. 2021

An electric pump costs P3,200, maintenance is P50/year, efficiency is 0.85, life 14 years, used 400 hr/year, electricity costs P0.04/kWh, and horsepower is 200 hp. Find monthly cost.

$$Annual\ cost=\frac{400(0.04)(200)(0.746)}{0.85}+50=2,858.47$$
$$Monthly\ cost=\frac{2,858.47}{12}=238.20$$

Final answer: P238.20 per month.

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