please solve by linear programming

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 most three in any one 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 it be 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 he paid. Once a mine has been closed it cannot be reopened. The yearly royalties payable cach mine kept 'open' are: Mine 1 5m Mine 2 4m Mine 3 4m Mine 4 5m There is an upper limit on the amount of ore which can be extracted from cach minc in one year. These upper limits are: Mine 1 2m lains Mine 2 2.5m tons Mine 3 1.3m tons Mine 4 3m tons The ore from the different mines is of varying quality. This quality is measured on a scale such that blending ores together results in a linear combination of the quality measurements, e.g. if equal quantities of two ores were combined the resultant ore would have a quality measurement half way between that of the two ingredient ores. Measured in these units the qualities of the ores from the mines are given below: Mine 110 Minc 20.7 Mine 3 1.5 Minc 40.5 To make this blending clearer il we blend a quantity from mine 1, b frumri mine 2, c frumri mine 3 and d from mine 4 the resulting blend has quality (1.02+0.75+1.50+0.5d)/(a+h+c+d). In each year it is necessary to combine the total outputs from each mine to produce a blended ore of exactly stipulated quality. For each year these qualities are: Year 10.9 Year 20.8 Year 3 1.2 Year 40.6 Year 5 1.0 The final blended ore sells for 10 per ton each year. Formulate a mixed integer programming problem to determine which mines should be operated each year and how much they should produce. Variables Objective Constraints Constraint 1 Constraint 2 Constraint 3 Constraint 4 Constraint 5 Constraint 6 Constraint 7 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 most three in any one 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 it be 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 he paid. Once a mine has been closed it cannot be reopened. The yearly royalties payable cach mine kept 'open' are: Mine 1 5m Mine 2 4m Mine 3 4m Mine 4 5m There is an upper limit on the amount of ore which can be extracted from cach minc in one year. These upper limits are: Mine 1 2m lains Mine 2 2.5m tons Mine 3 1.3m tons Mine 4 3m tons The ore from the different mines is of varying quality. This quality is measured on a scale such that blending ores together results in a linear combination of the quality measurements, e.g. if equal quantities of two ores were combined the resultant ore would have a quality measurement half way between that of the two ingredient ores. Measured in these units the qualities of the ores from the mines are given below: Mine 110 Minc 20.7 Mine 3 1.5 Minc 40.5 To make this blending clearer il we blend a quantity from mine 1, b frumri mine 2, c frumri mine 3 and d from mine 4 the resulting blend has quality (1.02+0.75+1.50+0.5d)/(a+h+c+d). In each year it is necessary to combine the total outputs from each mine to produce a blended ore of exactly stipulated quality. For each year these qualities are: Year 10.9 Year 20.8 Year 3 1.2 Year 40.6 Year 5 1.0 The final blended ore sells for 10 per ton each year. Formulate a mixed integer programming problem to determine which mines should be operated each year and how much they should produce. Variables Objective Constraints Constraint 1 Constraint 2 Constraint 3 Constraint 4 Constraint 5 Constraint 6 Constraint 7