Linear Programming (LP) is a powerful mathematical technique that can be used as a tool in Life Cycle Assessment (LCA). In the Inventory and Impact Assessment phases, in addition to calculating the environmental impacts and burdens, it can be used for solving the problem of allocation in multiple-output systems. In the Improvement Assessment phase, it provides a systematic approach to identifying possibilities for system improvements by optimising the system on different environmental objective functions, defined as burdens or impacts. Ultimately, if the environmental impacts are aggregated to a single environmental impact function in the Valuation phase, LP optimisation can identify the overall environmental optimum of the system. However, the aggregation of impacts is not necessary: the system can be optimised on different environmental burdens or impacts simultaneously by using Multiobjective LP. As a result, a range of environmental optima is found offering a number of alternative options for system improvements and enabling the choice of the Best Practicable Environmental Option (BPEO). If, in addition, economic and social criteria are introduced in the model, LP can be used to identify the best compromise solution in a system with conflicting objectives. This approach is illustrated by a real case study of the borate products system.