Use dynamic programming to find the shortest path for delivering products from Atlanta to Detroit. $($Define stages, states,

and decisions and show all tables and final solution$)$

Trucks with limited transportation capacity of $1000$ products are used to transport the goods and the transportation cost is $2($$$/$hour

per product$).$ The table below shows other costs and capacities. Minimum demand in Detroit and Pittsburgh are $5000$ and $4000$

accordingly.

Plants Production Cost $($$$)$ Production Capacity

Atlanta $83000$

Birmingham $66000$

Part b$)$ Formulate the problem as a linear programming model to find the best logistic strategy for this supply chain. $($Just formulation,

no need to solve it$)$