Consider again the original problem $($i$.$e$.$ supply in Pittsburgh is $180$ units and there are no storage or

production costs$).$ Now suppose that the supply at plant $2($Memphis$)$ decreased from $280$ to $250$

creating excess of total demand over total supply. The following table provides the cost per unit that

GBC incurs for not satisfying demand at each warehouse $($the costs are incurred because of penalties

built into contracts with customers served by each warehouse$).$

Warehouse $12345$

Cost per unit of unsatisfied demand $$0\mathrm{.}15$ $$0\mathrm{.}10$ $$0\mathrm{.}25$ $$0\mathrm{.}20$ $$0\mathrm{.}05$

Modify the original network structure$/$graph and the corresponding LP model to determine the shipping

plan that will have the minimum total costs $($in this case total costs include shipping costs & shortage costs$)$