QUESTION $1$ : FCC Company supplies corn from three silos $($represented by the nodes $1,2,$ and $3)$ to three

poultry farms $($represented by the nodes $4,5,$ and $6).$ The supply amounts at the silos $1,2,$ and $3$

are $100,200,$ and $50$ tons of corn, respectively, and the demand at the farms $4,5,$ and $6$ are $150,$

$80,$ and $120$ tons of corn, respectively. The transportation costs per ton of corn and the minimum

and maximum capacity on each arc are given in the table below.

Pag e $2|3$

$($a$)$ What type of network problem is described above?

$($b$)$ Draw a network to illustrate the problem.

$($c$)$ Formulate the problem as a linear programming model. That is$,$ define the decision

variables explicitly, write the mathematical expressions for the objective function and

constraints in OPEN FORM, and explain them clearly.