Thermodynamic processes at the microscale are characterized by non-negligible fluctuations of quantities such as heat and work. The range of values over which these quantities may fluctuate is called the support of the process and plays a decisive role in its operational properties. A natural question, therefore, is to ask which support optimizes a given thermodynamic task. In this presentation I will first discuss some recent results in the literature which touch upon this topic. Then I will move on to show how this problem may be cast in the language of Linear Programming, a mathematical optimization method that allows for both analytical as well as efficient numerical solutions. As an application, we discuss how our method can be used to derive the so-called Thermodynamic Uncertainty Relations (TUR) and generalizations.