Consider the following linear programming problem
Max z = 3A + 2B
s.t.
1A + 1B <=10
3A + 1B <= 24
1A + 2B <=16
A,B >=0
Suppose that the computer printout give you the following information related to the dual price
|
Constraint 1
|
RHS Value
|
Allowable Increase
|
Allowable Decrease
|
|
1
|
10
|
1.2
|
2
|
|
2
|
24
|
6
|
6
|
|
3
|
16
|
Infinite
|
3
|
The dual value for constraint 1 is 0.5. Explicitly express how the optimal objective function value of z = 27 would change if the right hand side of constraint 1 is increased by 1 unit. Specifically, state the new value of z.
Similarly, suppose that the right hand side value of constraint 1 is decreased by 2 units. Specifically, state how the optimal objective function value of z = 27 would change if the right hand side of constraint 1 is increased by 1 unit. State the new value of z.
To answer this question you should follow and specific script. First state if the change to the right hand side is within the range. If the change is within the range, what does this mean for the dual price?
Specifically, is the current dual price valid or not. If the dual price remains valid, calculate the new z-value with the specified change. If the dual price is not valid, you must resolve the problem.
(Make sure you explain in full detail almast as if you were writing a text book)