The most profitable use of a manufacturing company's scarce machine time occurs when the company is operating in the most efficient manner. The product mix problem of XYZ Company, a manufacturer of suits, jackets and trousers is used in this paper to illustrate the real-life application of the Simplex methodology of linear programming. The processing time, weekly station capacity, demand limits, selling prices and raw material costs are from a published case study. The goal is to determine the optimal level of production for each product per week in order to maximize profit. The model contains 3 decision variables, 11 constraints: 8 production stations and 3 demand limits. This was solved by using the Simplex tableau iterations and verified using the Microsoft Excel Solver. The best plan is to sell 476.23 suits, 753.75 jackets, and 600 trousers each week and the maximum weekly profit is ₺612,017.30. The demand limit for trousers is fully utilized and two stations are used: Model Preparation and Slaughterhouse. The shadow prices indicate that an additional minute at Slaughterhouse contributes approximately ₺236.31 to the weekly profit, whereas the other six stations have idle time. The results reveal that the Simplex method not only provides a production plan, but also provides a definite direction as to where additional capacity is worth purchasing.