The Special Motors Corporation $($SMC$)$ specializes in the production of a single type of car. SMC currently has four plants that manufacture and assemble the cars and then distribute them to two warehouses $($for subsequent distribution to individual dealers$).$ The relevant information is summarized in the table below:

Unit transportation Anual Production Annual Fixed

costs $($in dollars$)$ Capacity Operating Cost

Warehouse $1$ Warehouse $2($in $1000$ cars$)($in $$1000)$

Plant $1671618306$

Plant $2587824140$

Plant $337663188$

Plant $4155422164$

Annual

Demand $1733$

$($in $1000$ cars$)$

The top management of SMC feels that closing of one or more plants would reduce fixed operating costs by more than the resulting increase in transportation costs from the remaining plants to the warehouses. Therefore, you have been asked to study the issue.