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Answer:
A parameter table was constructed to show the transportation problem and to also obtain an optimal solution.
Explanation:
<u>Solution</u>
(a) the first step is to prepare the problem as a transportation problem by establishing the appropriate parameter table
1 2 3 Supply
Source 1 31 45 38 400
(Plant) 2 29 41 45 600
3 32 46 40 400
4 28 42 M 600
5 29 43 M 1000
Demand 600 1000 800
The total supply is = 400 + 600 + 400+ 600+ 1000= 3000
Total demand is = 600 + 1000 + 800 = 2400
(b) since the problem given is an imbalanced transportation problem,to make it a balance transportation problem we will make use of what is called the dummy destination for this numbers 3000 - 2400 = 600
1 2 3 4 (Dummy) Supply
Source 1 31 45 38 0 400
(Plant) 2 29 41 45 0 600
3 32 46 40 0 400
4 28 42 M 0 600
5 29 43 M 0 100
Demand 600 1000 800 600
The positive independent number of allocations is equal to m+n -1 = 5 + 4-1 =8
This solution is a basic feasible solution called a non -degenerate
The cost of initial transportation is he initial transportation cost=31*400+29*200+41*400+46*400+42*200+M*400+M*400+0*600
=$61400+800M
Note: kindly find an attached document of the part of the solution of the work.
