Solution of linear programming by 

Graphical Method

Part a)  The formulation is provided below

X1 = number of generators X2 = number of alternators
Maximize  250 X1 + 150 X2  (Objective Function)
With Constrainsts 2X1 + 3X2 ≤ 260  Wiring Time ( Hours)
1X1+ 2X2≤  140  Testing Time  ( Hours)
X1≥0 X2≥0  Part

b) sketching the  problem & Identifying 

feasible regions Points for  2x1 + 3x2 =260 Points  for 1X1 +2X2 =140 x1  x2 = (260-2x1)/3 x1 X2 =(140-x1)/2 

The assignment problem is one of the cordinal combinatorial optimization problems in the branch of optimization or operations research in mathematics. It check of finding a high weight matching in a weighted bipartite graph.

Assignment problem.
Input: predetermine, complete maney sides graph G = (L ??R, E)
with |L| = |R|.
Goal: find a perfect matching of minimum weight.

1- 3 8 9 15 10
2 – 4 10 7 16 14
3 - 9 13 11 19 10
4 - 8 13 12 20 13
5 - 1 7 5 11

1' 2' 3' 4' 5'
Min cost perfect matching
M = { 1-2', 2-3', 3-5', 4-1', 5-4' }
cost(M) = 8 + 7 + 10 + 8 + 11 = 44
Following are some of the areas in Operations Management in which we provide help
Solution of the assignment problem :-

1 COMPLETE ENUMERATION METHOD
2 TRANSPORTATION METHOD
3 SIMPLEX METHOD
4 HUNGARIAN ASSIGNMENT METHOD (HAM)
5 SOME MORE SPECIAL CASES
6 DUALITY

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