Question 4: The Makonsel company is a fully connected supply chain that produces goods in production centers (Atlanta, Birmingham, and Nashville) and sells them at its markets or retail outlets in Pittsburgh, Detroit, and Richmond. After production, the goods are stored in one of the warehouses in Nashville and Memphis and then they are sent to one of the cities in Indianapolis, Columbus, or Richmond for final delivery. The possible logistic paths and their travel times (hrs) are listed in the table below:

	Nashville	Memphis	Indianapoli	Columbus	Richmond	Pittsburgh	Detroit
Atlanta	4	3
Birmingham	3	6
Nashville			5	6	9
Memphis			7	9	12
Indianapolis						6	3
Columbus						3	3
Richmond						6	9

Part a) Use dynamic programming to find the shortest path for delivering products from Atlanta to Detroit. (Define

stages and states, show all tables and final solution)

The tables below show other costs and capacities. The transportation cost is 0.01 ($/hour per product).

Plants	Production Cost ($)	Production Capacity
Atlanta	8	3000
Birmingham	6	6000
Nashville	5	1000

Markets	Min Demand	Product Price ($)
Detroit	5000	100
Pittsburgh	3000	50
Richmond	2000	60

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

Part c) Use software to solve the problem (Show the screen shot of the setting window and results)

Part d) Investigate the effects of transportation capacity on total profit (Be creative, no specific requirement)

Part e) If we assume that there is also another option to send items by airplane from plants to markets with total costs

(production + transportation) listed in the below table, use transportation simplex to find optimal transportation plan (You

need to ignore intermediate stages and only focus on demand and supply data listed in the tables)

	Detroit	Pittsburgh	Richmond
Atlanta	12	10	11
Birmingham	9	8	7
Nashville	8	7	6