Transportation Problem $(2-$stage$-$transport$)$

Minimize the costs of shipping goods from factories to warehouses and customers, and

warehouses to customers, while not exceeding the supply available from each factory or

the capacity of each warehouse, and meeting the demand from each customer.

Cost of shipping $($$ per product$)$

Destinations

Warehouse $1$ Warehouse $2$ Warehouse $3$ Warehouse $4$

Factory $1$ $$0\mathrm{.}50$ $$0\mathrm{.}50$ $$1\mathrm{.}00$ $$0\mathrm{.}20$

Factory $2$ $$1\mathrm{.}50$ $$0\mathrm{.}30$ $$0\mathrm{.}50$ $$0\mathrm{.}20$

Customer $1$ Customer $2$ Customer $3$ Customer $4$ Customer $5$

Factory $1$ $$1\mathrm{.}75$ $$2\mathrm{.}50$ $$1\mathrm{.}50$ $$2\mathrm{.}00$ $$1\mathrm{.}50$

Factory $2$ $$2\mathrm{.}00$ $$2\mathrm{.}50$ $$2\mathrm{.}50$ $$1\mathrm{.}50$ $$1\mathrm{.}00$

Customer $1$ Customer $2$ Customer $3$ Customer $4$ Customer $5$

Warehouse $1$ $$1\mathrm{.}50$ $$1\mathrm{.}50$ $$0\mathrm{.}50$ $$1\mathrm{.}50$ $$3\mathrm{.}00$

Warehouse $2$ $$1\mathrm{.}00$ $$0\mathrm{.}50$ $$0\mathrm{.}50$ $$1\mathrm{.}00$ $$0\mathrm{.}50$

Warehouse $3$ $$1\mathrm{.}00$ $$1\mathrm{.}50$ $$2\mathrm{.}00$ $$2\mathrm{.}00$ $$0\mathrm{.}50$

Warehouse $4$ $$2\mathrm{.}50$ $$1\mathrm{.}50$ $$0\mathrm{.}20$ $$1\mathrm{.}50$ $$0\mathrm{.}50$

Warehouse $1$ Warehouse $2$ Warehouse $3$ Warehouse $4$

Capacity $45,00020,00030,00015,000$

Factory Capacity

Factory $160,000$

Factory $260,000$

Customer $1$ Customer $2$ Customer $3$ Customer $4$ Customer $5$

Demands $30,00023,00015,00032,00016,000$