Feeding cattle with on-pasture supplementation or feedlot diets can increase animal efficiency and system profitability while minimizing environmental impacts. However, cattle system profit margins are relatively small and nutrient supply accounts for most of the costs. This paper introduces a nonlinear profit-maximizing diet formulation problem for beef cattle based on well-established predictive equations. Nonlinearity in predictive equations for nutrient requirements poses methodological challenges in the application of optimization techniques. In contrast to other widely used diet formulation methods, we develop a mathematical model that guarantees an exact solution for maximum profit diet formulations. Our method can efficiently solve an often-impractical nonlinear problem by solving a finite number of linear problems, that is, linear time complexity is achieved through parametric linear programming. Results show the impacts of choosing different objective functions (minimizing cost, maximizing profit and maximizing profit per daily weight gain) and how this may lead to different optimal solutions. In targeting improved ration formulation on feedlot systems, this paper demonstrates how profitability and nutritional constraints can be met as an important part of a sustainable intensification production strategy.

用牧草补充饲料或育肥场饲喂牛可以提高动物效率和系统利润，同时将对环境的影响降至最低。但是，养牛系统的利润率相对较小，而养分供应占了大部分成本。本文基于已建立的预测方程，介绍了肉牛的非线性最大化利润的日粮配方问题。营养需求量预测方程中的非线性因素对优化技术的应用提出了方法上的挑战。与其他广泛使用的饮食配方方法相反，我们开发了一个数学模型，可以保证为最大利润的饮食配方提供精确的解决方案。通过解决有限数量的线性问题，我们的方法可以有效地解决通常不切实际的非线性问题，即 线性时间复杂度是通过参数线性编程实现的。结果显示了选择不同目标函数（最小化成本，最大化利润和最大每日增重利润）的影响，以及这如何导致不同的最佳解决方案。在以饲养场系统上的改良日粮配方为目标的过程中，本文证明了如何满足利润率和营养限制，将其作为可持续集约化生产战略的重要组成部分。