Clifton Springs $1$ $$32$ $$34$ $$32$ $$40$

Danville $2$ $$34$ $$30$ $$28$ $$38$

The plant capacities and customer orders are as follows.

Plant Capacity $($units$)$

Clifton Springs $5,000$

Danville $3,000$

Distributor Orders $($units$)$

D$1$

$2,000$

D$2$

$5,000$

D$3$

$3,000$

D$4$

$2,000$

$($a$)$

Develop a network model and a linear programming formulation of this problem.

$($i$)$

network model $($Submit a file with a maximum size of $1$ MB$.)$