1) What is the value for an additional unit of each resource? 2) Over what range
ID: 324942 • Letter: 1
Question
1) What is the value for an additional unit of each resource?
2) Over what ranges are the values in question #1 (above) valid?
MAX Z = 9000X1 + 12000X2
X1 X2 RHS Dual
Maximize 9000 12000
Solution-> 4 6 108000
Variable Value Reduced Cost Original Val Lower Bound Upper Bound
X1 4 0 9000 6000 12000
X2 6 0 12000 9000 18000
Constraint Dual Value Slack/Surplus Original Val Lower Bound Upper Bound
Constraint 1 750 0 64 57.1429 68
Constraint 2 1200 0 50 45 52.7273
Constraint 3 0 12 120 108 Infinity
Constraint 4 0 3 7 4 Infinity
Constraint 5 0 1 7 6 Infinity
Variable Status Value
X1 Basic 4
X2 Basic 6
slack 1 NONBasic 0
slack 2 NONBasic 0
slack 3 Basic 12
slack 4 Basic 3
slack 5 Basic 1
Optimal Value (Z) 108000
Explanation / Answer
1) Value of each additional unit of each resource is indicated by dual value.
Dual value of constraint 1 is 750 , so it is the value of additional unit of resource 1
Similarly, value of addtional unit of resource 2 is 1200
2) These values are valid in the range of lower bound and upper bound
Therefore, dual value of resource 1 (=750) is valid within the range of 57.1429 to 68
Similarly, the feasible range for dual value of resource 2 is from 45 to 52.7273
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