Break-even with line cutting method

摘要

Any firm has the plan for profit to running business. The profit or loss is from the difference between the revenue and the cost. Generally, the revenue is from sales volumes multiplied by unit price (R = PQ) and the cost is from the fixed cost plus unit variable cost multiplies by sales volume (C = VQ + F). The break-even point of sales amount or sales volume is when the revenue equal to the cost (R = C). The plan for profit could be given when the revenue over the cost, but may have lose when the revenue under the cost (π = R-C = (P-V)Q-F, π (profit) ≦ 0 or π (loss) ≧ 0). The linear model is that the sales volumes are not relation to the unit price and to the unit variable cost. In the practical field, the quadratic model is instead of the linear model. The profit (loss) on the quadratic form (π = R-C = Q(-aQ + b)-F) is from the difference between revenue (R = Q(-arQ + br)) and cost (C = (aeQ + bc) + F). There are does not linear relationship between the sales volume and the unit price and as same as unit variable cost. To find the break point of profit (loss) is given for the multi-products, the line cutting method be introduced to get the answer. In this paper, we developed the curve cutting method to solute the quadratic form for multi-products.