a$)$ Given the expected quantitiy transported from plants $({�}_1,{�}_2,{�}_3,{�}_4$ and $\{$:${�}_5)$ to awarehouse that will be located to serve all plants equating $100,120,80,150$ and $250$respectively, determine $�**$ and $�**$ coordinates of the warehouse by median approach andcenter of gravity approach.b$)$ Suppose we have three existing warehouses ${�}_1,{�}_2$ and ${�}_3$ whose demands equate $125,$$75$ and $200$ respectively, and whose locations are as $(5,10),(15,15)$ and $(20,20)$ respectivelyand five plants are given in $($a$)($i$.$e$.$ P$1$ located at $(5,5)$ has a supply capacity of $100$ units$).$ Forestimated unit transportation cost of $$5$ per unit distance per unit quantity transported,using Rectilinear distance, solve this transportation problem for optimal allocations ofplants to existing warehouses.

2. (0,0) P1 (5,5) P5 (10,20) P3 P4 (8,15) (20,15) P2 (20,5) (30,30) a) Given the expected quantitiy transported from plants (P1, P2, P3, P4 and P5) to a warehouse that will be located to serve all plants equating 100, 120, 80, 150 and 250 respectively, determine x and y coordinates of the warehouse by median approach and center of gravity approach. b) Suppose we have three existing warehouses W1, W2 and W3 whose demands equate 125, 75 and 200 respectively, and whose locations are as (5,10), (15,15) and (20,20) respectively and five plants are given in (a) (i.e. P1 located at (5,5) has a supply capacity of 100 units). For estimated unit transportation cost of $5 per unit distance per unit quantity transported, using Rectilinear distance, solve this transportation problem for optimal allocations of plants to existing warehouses.