the plan of lowest breakeven point has the maximum ability of taking a risk,it s a first priority plan;the plan of highest berakeven point has the minimum ability of taking a risk,it s a obsoleted plan.

Based on analysis of the defects of basic break even graph, adopting volume profit graph to sensitivity analysis of profit gauge is proposed.

And the break-even point is that the extraction rate of gold is more than 50.

Taking complete cost model as benchmark,this paper analyzed the price of natural gas at break-even point when producing synthesized ammonia,methanol,butyloctanol,and hydrogen with natural gas as raw material,and raised the proposals on reducing natural gas cost and widening its applying range.

The train s utilized rate of break-even point was obtained based on the analysis of real example.

As there are disadvantages in the traditional three stage selection mining technique,the paper accepts the breakeven point method and value engineering method used in engineering economy,and changes the previously qualitative comparison into quantitative analysis.

And by calculation the feasible breakeven point is obtained.

The Paper expounds the basic principles of cost and efficiency analysis for invested project,analyses the principle and process with mathematical methods and graphs directly and simply,and illustrates the comparison and analysis of cost and efficiency among different cases by means of breakeven point with examples.