Catch & Release $($C&R$)$ Co$.$ produces fly boxes. C&R has two small plants. C&R supplies their items to four fly fishing shops. There are three warehouses to stop by$.$ The shipping cost is calculated as following:

Shipping cost $=$$$1$ the number of boxes $$ the distance

Plant $1$ and plant $2$ can produce up to $1000$ items and $800$ items respectively. And warehouses also have their capacities, $800,600,700$ and $500$ items for warehouse $1,2,3$ and $4,$ respectively.

Fly fishing shops order $300,500,400$ and $600$ items for shop $1,2,3$ and $4,$ respectively.

$P_{ij}$ : Shipment$($No$.$ of items$)$ from plant ito Warehouse $j$

$W_{\frac{?}{\text{b}\text{a}\text{r}}(j)}$ : Shipment$($No$.$ of items$)$ from Warehouse $i$ to fly shop $j$

A$.(5$ points$)$ Write Objective Function using decision variables that defined above $($Start with MAX or MIN$)$

B$.(10$ points$)$ Write all the constraints.

C$.$ Create a Spreadsheet model of the problem on Excel and find the optimal solutions for $P_{ij}$ and $W_{ij}($Make sure you generate Sensitivity report$)$

D$.(5$ points$)$ What is the Optimal total cost?

E$.(20$ points$)$ The CEO wants to add the new plant because the total capacity of C&R$\text{'}$s two plants are barely supply the flyboxes. Since the warehouse $2$ and $3$ get the flyboxes only from one plant, the new plant will supply the flyboxes only to warehouse $2$ and $3.$ The third plant will have the capacity, $600.$ New network with the third plant would be like the picture below. The cost of the third plant would be $$5,000.$ Would it be economically benificial to get the third plant? F$.(20$ points$)$ The CEO insists that C&R have the third plant. Now, after investigating the supply network, she siad "I believe we have too many warehouse compared to the number of shops. can we save some money by closing one or two of our warehouse?", As an supply chain analyst, you should find out what would be the best option for C&R$,$ Do not close any warehouse, close one or close two? If we need to close one or two which one should we close? The fixed cost to open the warehouses $1,2,3$ and $4$ are $$3,400,$$$4,000,$ $$3,600$ and $$3,000,$ respectively.