PureCoffee

$0\mathrm{.}0/8\mathrm{.}0$ points $($graded$)$

PureCoffee imports highest grade coffee beans from Africa and South America. They roast the beans tenderly using a novel process to create a unique taste of coffee. Pure Coffee serves three markets $($M$1,$ M$2,$ and M$3)$ in Europe. Market demand for the next week is given in the following table.

Market Demand $($tons per week$)$

Market $1($M$1)500$

Market $2($M$2)1000$

Market $3($M$3)500$

To serve Europe they have two roasting plants available $-$ one in the North of Europe $($N$)$ and one in the South of Europe $($S$).$

Roasting Plant Capacity $($tons per week$)$

North $($N$)1000$

South $($S$)1000$

Currently they are using two distribution centers in Europe to connect the roasting plants with markets. They ship the roasted beans from the production sites to the distribution centers and distribute from there to three different markets.

The cost to transport a ton of roasted beans from a roasting plant to a dibstrution center and from the distribution center to the customers depends on the distances between the different locations. These costs are given in the two tables below:

Origin: Roasting Plant Destination: Distribution Center Transportation Cost $($Euros$/$ton$)$

North $($N$)$ Distribution Center A $54$

Distribution Center B $46$

South $($S$)$ Distribution Center A $52$

Distribution Center B $40$

Origin: Distribution Center Destination: Market Transportation Cost $($Euros$/$ton$)$

Market $166$

Distribution Center A Market $274$

Market $366$

Market $176$

Distribution Center B Market $252$

Market $344$

PureCoffee wants to minimize the total weekly cost. They ask you to optimize the roasted beans flow from the processing facilities to their customers.

In the optimal solution, what is the minimum total weekly cost of moving roasted beans from roasting plants to customers? Enter your answer in Euros without a currency symbol.