Question: GMC produces custom metal alloys from ores produced from 6 mines. The ores contain copper, tin, lead and zinc and impurities. GMC has just received an order for 1000 tons of an a metal alloy which is at least 21% copper, no more than 12% tin, no more than 7% lead and between 30% and 65% zinc. The portion of each metal and cost/ton from each mine is given in the table below:
Mine Copper Tin Lead Zinc $/ton
1 19% 15% 12% 14% 27
2 43% 10% 25% 7% 25
3 17% 0% 0% 53% 32
4 20% 12% 0% 18% 22
5 0% 24% 10% 31% 20
6 12% 18% 16% 25% 24

How much ore should be obtained from each mine to meet the alloy order at minimum cost?