A gold mining company extracts gold from mine A and mine B. Both mines produce three grades of gold: high, medium, and low. The cost to mine a ton of gold from mine A is $300, and from mine B, it is $200. Mine A yields 4 tons of high-grade gold for each day of operation, and mine B yields 3 tons. Both mines yield 2 tons each of medium-grade gold each day. The yield each day for low grade gold is 5 tons from mine A and 8 tons from mine B. The company has contracted with a gold processor to supply at least 6 tons of high-grade gold, 4 tons of medium-grade gold, and 12 tons of low-grade gold. How many tons of gold from both mines must be extracted each day to minimize the total cost subject to the above constraints?