The Medequip Company produces precision medical diagnostic equipment at two factories. Three medical centers have placed orders for this month$$s production output. The table below shows what the cost would be for shipping each unit from each factory to each of these customers. Also shown are the number of units that will be produced at each factory and the number of units ordered by each customer.

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A decision now needs to be made about the shipping plan for how many units to ship from each factory to each customer. $($e$.$g$.,$ x$11$ means units from Factory $1$ to Customer $1)$

$($a$)$ Formulate a linear programming model for this problem.

$($b$)$ Solve this model in GAMS$/$Excel$.$