Solve the folloiwng problem:
Q. In the transportation problem , products are produced at plants in Locations A and B and shipped to warehouses in locations X, Y and Z.
a. According to the model formulation, what is the capacity of Plant B? _________
b. According to the model formulation, what is the demand at warehouse Z? ___________
c. According to the model formulation, what is the shipping cost for sending products from Plant A to Plant B?
d. According to the solution, how many products should be shipped from Plant A to Plant B?
e. At what point would more products would be shipped from Plant A to Warehouse Y?______
f. What would be the total shipping cost if the demand at warehouse Z was equal to 600?_____
g. At what point would less products would be shipped from Plant B to warehouse Z?______
h. What would be the total shipping cost if the capacity of Plant B was equal to 700? ________
i. At what point would some units be shipped from Plant A to warehouse X? ____________
j. Would the current solution remain optimal if the shipping cost from Plant A was $9, $8.75 and $14 to warehouses X, Y, and Z, respectively? Demonstrate.MIN 11AX+8AY+12AZ+1.5AB+6BX+8BY+5BZ+1YZ
S.T.
1) 1AX+1AY+1AZ+1AB<1200
2) -1AB+1BX+1BY+1BZ<600
3) 1AX+1BX>500
4) 1AY+1BY-1YZ>600
5) 1AZ+1BZ+1YZ>700
OPTIMAL SOLUTION
Objective Function Value = 12200.000
Variable Value Reduced Costs
AX 0.000 3.500
AY 600.000 0.000
AZ 0.000 5.500
AB 600.000 0.000
BX 500.000 0.000
BY 0.000 1.500
BZ 700.000 0.000
YZ 0.000 2.500
Constraint Slack/Surplus Dual Prices
1 0.000 0.000
2 0.000 1.500
3 0.000 -7.500
4 0.000 -8.000
5 0.000 -6.500
OBJECTIVE COEFFICIENT RANGES
Variable Lower Limit Current Value Upper Limit
AX 7.500 11.000 No Upper Limit
AY 5.500 8.000 9.500
AZ 6.500 12.000 No Upper Limit
AB 0.000 1.500 4.000
BX 1.500 6.000 9.500
BY 6.500 8.000 No Upper Limit
BZ 1.500 5.000 7.500
YZ 1.500 1.000 No Upper Limit
RIGHT HAND SIDE RANGES
Constraint Lower Limit Current Value Upper Limit
1 1200.000 1200.000 No Upper Limit
2 600.000 600.000 1200.000
3 0.000 500.000 500.000
4 0.000 600.000 600.000
5 100.000 700.000 700.000