A shoe factory predicts the following demands for its pairs of shoes for the next 2 months: 

May: 250, June: 300. The cost of manufacturing a pair of shoes is US$70.0 with normal working hours and $110.0 with working hours. overtime. During each month, normal-hour production is limited to 200 pairs of shoes and overtime production is limited to 100 pairs. Keeping a pair of shoes in inventory costs US$10.0 per month. The company seeks to meet demand by minimizing overtime work. Formulate a mathematical model that allows obtaining an optimal solution. Pose the problem as Transport (the problem consists of 4 origins and 2 destinations). Obtain the distribution of work that minimizes costs.