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Mining A mining company is going to continue operating in a certain area for the next five years. There are four mines in this area but it can operate at mest three in cach year. Although, a mine may not operate in a certain year it is still necessary to keep it "open", in the sense that royalties are payable, should I he operated in a future year. Clearly, if a mine is not going to be worked again it can be closed down permanently and no more royalties need be paid. The yearly royalties payable on cach mine kept "open" are: Mine 1 Mine 2 Mine 3 Mine 4 $5 million S4 million S4 million $5 million There is an upper limit to the amount of ore which can be extracted from cach mine in a year. These upper limits are: Mine! 2 x 10 tons Mine 2 25 x 10 tons Mine 3 1.3 x 10 tons Mine 4 3 x 10 tons The ore from different mines is of varying quality. The quality is measured on a scale so that blending ores together results in a linear combination of the quality measurements, e.gif equal quantities of two ores were combined the resultant ore would half a quality measurement half way between that of the ingredient ores. Measured in these units the quantities of the oves from the mines are given below. Mine Mine 2 Mine 3 Mine 4 1.0 0.7 1.5 0.5 In cach year it is necessary to combine the total outputs from each mine to produce a blended one of cxactly some stipulated quality. For each year these qualities are: Year 09 Year 2 08 Year 3 1.2 Year 4 06 Year 5 LO The final blended ore sells for $10 per ton cach year. Revenue and expenditure for future years must be discounted at a rate of 10% annually. Which mines should be operated each year and how much should they produce