Linear programming, assignment , VAM, MODI, stepping stone

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Problem 1)
a) An electrical manufacturing makes delta motors (X1) and Y- motors (X2). For this it has four operations -stamping , casting , wiring, and an assembly and testing. Each unit of a delta motor requires 2 hours in the stamping department, 3 hours in the wiring dept. and 1 hour for assembly and testing. Each Y-motor requires 2 hours in stamping, 3 hour in casting , 1 hour in wiring , an ½ hour for assembly & testing . The profit (in hundreds of dollars is 3$ for a delta motor and $3.6 for a Y-motor . The available capacity of each operation is below : (leave profit in hundreds of dollars)
Stamping 8 hours Wiring 7.5 hours
Casting 9 hours Assembly and testing 3 hours
Set up the LP problem , the first tableau, and solve for the objective row and the stub in the second tableau .
b)
X1 X2 X3 X4 X5 X6 -P Xb

X1 1 0 ½ -1/3 0 0 0 1
X2 0 1 0 1/3 0 0 0 3
X5 0 0
-3/2 2/3 1 0 0 3/2
X6 0 0 -1/2 1/6 0 1 0 1/2
-P 0 0 -3/2 -1/5 0 0 1 -69/5
Above is the third tableau . Discuss why this is optimal and give the answers
2) Determine the range of optimality .
3) Determine the range of feasibility
4) Discuss the implication of one half an hour more time available for wiring . Back your answer with figures.
5) If you had one hour less stamping , and one hour more casting time available , what would the solution be?
6) If the profit of the delta motors dropped from $3 to $2 .50 how would this change the outcomes ?
7) Set up the dual and give its answers
Problem 2.
Use the assignment method to determine the best way to assign workers to jobs , given the cost information below. Compute total cost for your assignment plan. JOB
A B C D E
1 7
7 6 9 3
2 6 9 8 7 5
3 5 6 9 8 10
4 8 9 7 5 6

Problem 3
Water is to be pumped from three wells to meet demands in five towns in such a way as minimize surcharge costs . In the table below , well capacities and town demands are expressed in gallons per hour . Determine an initial solution for the distribution of water from wells to towns.
SURCHARGE(CENT PER 100GALLON) TOWN
1 2 3 4 5
A 4 16 2 10 19 500
B 18 7 9 3 15 675
C 13 8 22 11 6 800
WELL DEMAND (GPH) 400 400 500 375 300

Use VAM , MODI , and stepping stone methods to calculate the least surcharge cost.
Set up the underlying linear programming problem.