A mining company extracts uranium ore from A, B and C plants located in different geographical locations, working 8 hours a day and seven days a week. Uranium ore obtained from these plants is classified according to quality as high, medium and low grade. Plant A extracts high, medium and low grade uranium 0.75, 0.25 and 0.50 tons per hour respectively, while Plant B extracts 0.25, 0.25 and 1.5 tons per hour. Only high and low grade uranium ore can be extracted from Plant C and hourly production is 0.5 and 1 tons respectively. This company has contracts with multiple firms to provide at least 60 tons of high grade, 24 tons of medium grade and 72 tons of low grade uranium oreweekly. Hourly cost of production in Plant A is 400TL, while in Plant B is 500TL. Production in Plant C is 2.5 times more expensive than production in Plant A.

Generate a linear programming model that minimizes the cost of producing uranium ore in order to meet the requirements of its contracts.