Profit Maximization Linear Programming

I need a clear, well-structured linear programming model that focuses on pure optimisation—specifically a profit-maximisation scenario. All coefficients, constraints and objective functions must be laid out transparently so the logic is easy to follow and modify later.

What I will hand over:
• A concise description of the business context, the decision variables involved, and any hard limits or relationships that must hold.

What I expect back:
• A fully formulated LP model (objective function and constraints) expressed in standard mathematical notation.
• A working solution file that can be run in either Excel Solver, LibreOffice Calc with Solver, Python (PuLP, Pyomo or similar) or another open-source tool—please specify your choice up front.
• A short write-up (one to two pages) explaining the results, shadow prices and any sensitivity insights so I can understand how profit responds to changes in key parameters.

Acceptance criteria:
• Objective function must explicitly maximise profit; no surrogate measures.
• The model must run and reproduce the optimal profit figure you report, with all constraints satisfied.
• Variables, constraints and assumptions must match the business context I provide; no unstated simplifications.

If you have experience tackling maximisation problems in optimisation software and can explain your results clearly, I’m ready to move quickly once we agree on the toolset.