You are given the following information:

And the following constraints: max lead time of 30 days, max of 6 production plants, exactly 8 total markets, min of 700 tons of square capacity excess

Find the optimal solutions that MINIMIZES costs (give objective function, decision variables in your solution)

Landed Cost Production + Transport + Import Tax) per Ton Production/Market Country 1 Country2 Country3 Country Country5 Country6 Country7 Country8 Country 1 $4,840 $4,900 $5,4841 $5,501 $5,182 $5,050 $5,152 $5,172| Country 2 $5,250 $5,180 $5,838 $5,872 $5,415 $5,350 $5,509 $5,519 Country 3 $5,030 $5,508 $4,880 $5,625 $5,236 $5,080 $5,030 $5,314 Country 4 $5,020 $5,504 $5,594 $4,940 $5,198 $5,140 $5,020 $5,297 Country 5 $5,191 $5,708 $5,788 $5,830 $5,071 $5,311 $5,211 $5,425 Country 6 $5,423 $5,655 $5,775 $5,776 $5,463 $5,050 $5,170 $5,493 Country 2 Country 3 Country 4 Country 5 Country 6 425 - Quarterly Production Parameters Supply Chain Matrix (tons) Operating? Capacity Fixed Op. Cost Production/Market Country 1 1.00 1,725 $1,380,000 Country 1 1,120 1.00 800 $1,050,000 Country 2 1.00 5,286 $3,171,600 Country 3 1.00 483 $618,240 Country 4 1.00 1,050 $1,785,000 Country 5 1.00 2,334 $1,633,800 Country 6 Supply to Market 1,120 Demand in Tons 3,225 - - - 292 - | Country 7 Country 8 Production Total 1,120 425 247 180 3,652 292 684 - 2,065 247 180 247 180 684 425 425 | 3,225 3,225 292 292 684 684 2,065 2,065 2,065 20 Lead Time Matrix (Order Processing and Transportation) Days Production/Market Country 1 Country 2 Country 3 Country 4 Country 5 Country 6 Country 7 Country 8 Country 1 7 18 24 14 31 31 - 14| 39 Country 2 - 12 71 15 12 25. - 12 25 Country 3 16 15 7 16 27 25 16 29 Country 4 18 20 27 31 21 21 33 Country 5 31 38 38 38 7 38 38 24 Country 6 36 40 33 32 44 7 40 49 Max Lead Time 30 Landed Cost Production + Transport + Import Tax) per Ton Production/Market Country 1 Country2 Country3 Country Country5 Country6 Country7 Country8 Country 1 $4,840 $4,900 $5,4841 $5,501 $5,182 $5,050 $5,152 $5,172| Country 2 $5,250 $5,180 $5,838 $5,872 $5,415 $5,350 $5,509 $5,519 Country 3 $5,030 $5,508 $4,880 $5,625 $5,236 $5,080 $5,030 $5,314 Country 4 $5,020 $5,504 $5,594 $4,940 $5,198 $5,140 $5,020 $5,297 Country 5 $5,191 $5,708 $5,788 $5,830 $5,071 $5,311 $5,211 $5,425 Country 6 $5,423 $5,655 $5,775 $5,776 $5,463 $5,050 $5,170 $5,493 Country 2 Country 3 Country 4 Country 5 Country 6 425 - Quarterly Production Parameters Supply Chain Matrix (tons) Operating? Capacity Fixed Op. Cost Production/Market Country 1 1.00 1,725 $1,380,000 Country 1 1,120 1.00 800 $1,050,000 Country 2 1.00 5,286 $3,171,600 Country 3 1.00 483 $618,240 Country 4 1.00 1,050 $1,785,000 Country 5 1.00 2,334 $1,633,800 Country 6 Supply to Market 1,120 Demand in Tons 3,225 - - - 292 - | Country 7 Country 8 Production Total 1,120 425 247 180 3,652 292 684 - 2,065 247 180 247 180 684 425 425 | 3,225 3,225 292 292 684 684 2,065 2,065 2,065 20 Lead Time Matrix (Order Processing and Transportation) Days Production/Market Country 1 Country 2 Country 3 Country 4 Country 5 Country 6 Country 7 Country 8 Country 1 7 18 24 14 31 31 - 14| 39 Country 2 - 12 71 15 12 25. - 12 25 Country 3 16 15 7 16 27 25 16 29 Country 4 18 20 27 31 21 21 33 Country 5 31 38 38 38 7 38 38 24 Country 6 36 40 33 32 44 7 40 49 Max Lead Time 30