Four hospitals $(1,2,3,4)$ have their requirements for blood met through a central blood distribution office that coordinates deliveries from three blood banks $($A$,$ B$,$ and C$)$ on a weekly basis. The costs to ship a standard pouch of blood from each blood bank to each hospital are reported in the table below. The table also provides, for an upcoming week, the weekly number of pouches available at each blood bank and the number of pouches required, i$.$e$.$ the demand, at each hospital.

Blood BankHospitalPouches Available$1234$A$$2$$$4$$$6\mathrm{.}5$$$5\mathrm{.}5150$B$$4\mathrm{.}9$$$6\mathrm{.}9$$$5\mathrm{.}1$$$4\mathrm{.}5200$C$$5\mathrm{.}5$$$2\mathrm{.}5$$$3\mathrm{.}4$$$6320$Demand$40240100190$

Develop the optimization model that obtains an optimal shipment plan that ensures that capacities at warehouses are not violated and demands are met exactly. Compute the optimal shipment cost by solving the model using an optimizer such as EXCEL's Solver.

$($Specify as a whole number$)$