Pemodelan Matematika dalam Mengoptimalkan Hasil Produksi pada Toko Yani Cake di Kabupaten Klaten dengan Metode Big M

To improve community income and welfare, there needs to be direct involvement in economic development. The community can participate actively through engagement in Micro, Small, and Medium Enterprises. One of the challenges faced by Micro, Small, and Medium Enterprises, particularly in the culinary sector such as Yani Cake Shop in Klaten Regency, is making optimal production decisions given limited available resources. This study aims to optimize the daily production output of the six most popular types of cookies sold at the shop by using a mathematical modeling approach through the Big M method. The model is formulated based on an objective function to maximize daily revenue and constraint functions that represent the limitations of raw material stock and minimum production targets. Data were collected through direct interviews and processed using the PM Calculators website. As a result, the optimal daily production combination consists of 4 batches of nastar, 2 of putri salju, 2 of kastengel, 2 of donut cookies, 1 of lidah kucing, and 2 of peanut cookies, yielding an optimal sales value of IDR 2,155,000 per day. Additionally, a sensitivity analysis was conducted to assess the impact of changes in prices and raw material availability on the optimal solution.