3. Consider the following linear program:
MIN 6x1 + 9x2 ($cost)
s.t. x1 +2x2 ?8
10x1 + 7.5x2 ? 30
x2 ? 2
x1,x2 ?0
The Management Scientist provided the followingsolution output:
OPTIMAL SOLUTION
Objective Function Value = 27.000
Variable | Value | Reduced Cost |
X1 | 1.500 | 0.000 |
X2 | 2.000 | 0.000 |
Constraint | Slack/Surplus | Dual Price |
| 1 | 2.500 | 0.000 |
| 2 | 0.000 | ?0.600 |
| 3 | 0.000 | ?4.500 |
OBJECTIVE COEFFICIENT RANGES
Variable | Lower Limit | Current Value | Upper Limit |
X1 | 0.000 | 6.000 | 12.000 |
X2 | 4.500 | 9.000 | No Upper Limit |
RIGHT HAND SIDE RANGES
Constraint | Lower Limit | Current Value | Upper Limit |
| 1 | 5.500 | 8.000 | No Upper Limit |
| 2 | 15.000 | 30.000 | 55.000 |
| 3 | 0.000 | 2.000 | 4.000 |
A. What is the optimal solution including the optimal value ofthe objective function?
B .Suppose the unit cost of x1 is decreased to $4. Isthe above solution still optimal? What is
the value of the objective function when this unit cost isdecreased to $4?
C. How much can the unit cost of x2 be decreasedwithout concern for the optimal solution
changing?
D. If simultaneously the cost of x1 was raised to $7.5 and thecost of x2 was reduced to $6,
would the current solution still remain optimal?
E. If the right-hand side of constraint 3 is increased by 1,what will be the effect on the
optimal solution?
