### (Solved) The distribution system for the Herman Company consists of four plants, three warehouses and four customers

The distribution system for the Herman Company consists of four plants, three warehouses and four customers. Plant capacities and shipping costs per unit (in \$) from each plant to each warehouse are as follows:

______________________Warehouse
Plant_________1(5)_________2(6)_______3(7)__________Capactiy
1 ____________11 __________13 ________11___________ 500
2 ____________14 __________11 ________12___________ 550
3 ____________11__________ 12________ 11___________ 550
4 ____________13__________ 12________ 11___________ 500

Customer demand and shipping costs per unit (in \$) from each warehouse to each customer are as follows:

_________________________________Customer
Warehouse___________1(8) ____________2(9) ____________3(10) ____________4(11)
1(5) _________________8______________ 6______________ 10________________ 6
2(6)_________________ 5______________ 8_______________ 9________________ 9
3(7) _________________6______________ 8______________ 10________________ 7
Demand____________ 450 ____________500_____________ 450______________ 550

(a) Formulate the linear programming model–do not solve it.

(b) Suppose items can be shipped from Plant 3 (node 3) to customer 4 (node 11) at a cost of \$10 each, would you need to change the linear programming model)? If so, indicate all the changes you will need to make to the model you do not need to reformulate the entire model.