In the textile sector, seasonal demand fluctuations and variable raw material prices increase the strategic importance of production and inventory planning. In this study, a mathematical model has been developed to optimize the production and inventory planning for a three-month period of a textile company operating in Turkey. The model aims to minimize normal working hours, overtime, and inventory holding costs for three main product groups: T-shirts, trousers, and shirts. The mathematical model, solved using LINGO software, optimizes the company's three-month (June-August 2025) production and inventory planning. In the study, demand forecasts, labor requirements, minimum stock levels, and maximum storage capacity constraints were defined for each product. According to the optimization results, an optimal production and inventory plan was obtained with a total cost of 2,137,450 TL. This plan envisages production of 7,800 units for T-shirts, 4,200 units for trousers, and 4,650 units for shirts. Capacity utilization analysis showed that normal working hour capacity was utilized at 100%, while overtime capacity was used at 55% only in August for T-shirt production. Stock level analysis revealed that minimum stock levels were maintained for T-shirts and shirts, while high stock levels were maintained for trousers in June and July in preparation for high demand in August. Cost analysis showed that 91.3% of the total cost consisted of normal working hour production costs, 7.4% of overtime costs, and 1.3% of inventory holding costs. As a result of the study, strategic recommendations were presented regarding the company's production capacity management, inventory optimization, cost reduction, and demand management. The presented model is adaptable to other enterprises in the textile sector and provides a scientific approach to production and inventory planning decisions suitable for seasonal demand fluctuations.