Linear programming is a very useful decision tool when the decision is made from few alternatives but when a decision space exists. For instance, when a production plant wants to understand what is the optimal combinations of products. However, it is important to know that linear programming is only suitable where objectives and constraints are linear. If not, it would be an application of operational research to use non-linear programming possibly.
This is a very useful management tool to use the decision objectives to minimise cost or maximise profit by optimising the decision objective.
In my career, linear programming is a very useful tool especially redesigning a mechanical component to be optimised. For example, minimising a product weight can be the design objective which can be given by management to meet a certain strategic objective and specifying stiffness as the design constraint. This can optimise the component design to achieve the desired decision objective.