Solve the below:
Q: A manufacturing firm produces electric motors for washing machines and vacuum cleaners. The firm has resource constraints for production time, steel, and wire. The linear programming model for determining the number of washing machine motors (x1) and vacuum cleaner motors (x2) to produce that would maximize the profit has been formulated as follows:
maximise 30x1+40x2
st
2x1+3x2<=12(production time)
x1+4x2<=12(steel)
2x1+x2<=10(wire)
x1,x2>=0
The final optimal simplex tableau for this model is as follows:
|
Cj
|
Basic
Variables
|
|
30
|
40
|
0
|
0
|
0
|
|
Quantity
|
X1
|
X2
|
SI
|
S2
|
S3
|
|
30
|
xl
|
4.5
|
1
|
0
|
-0.25
|
0
|
0.75
|
|
40
|
x2
|
1
|
0
|
1
|
0.5
|
0
|
-0.5
|
|
0
|
s2
|
3.5
|
0
|
0
|
-1.75
|
1
|
1.25
|
|
|
xj
|
175
|
30
|
40
|
12.5
|
0
|
2.5
|
|
|
cj-zj
|
|
0
|
0
|
-12.5
|
0
|
-2.5
|
A. Formulate the dual for this problem.
B. What do the dual variables equal, an what do they mean?
C. Determine the sensitivity range for the profit from washing machine motors (c1) using the optimal tableau. Show your work.
D. Determine the feasible ranges for production hours (q1) and pounds of steel (q2) using the optimal tableau. Show your work.
E. What are the values of resources (production time, steel, and wire) that are utilized to produce (1) one washing machine motor, (2) one vacuum cleaner motor?