1) What is the value for an additional unit of each resource? MAX Z = 9000X 1 +
ID: 324941 • Letter: 1
Question
1) What is the value for an additional unit of each resource?
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) The value of additional unit of each resource is indicated by the Dual value of the constraints.
The value of additional unit of resources 1 (grapes) and 2 (storage) are 750 and 1200 respectively.
Value of additional unit of all other resources [resource 3 (processing time), 4 demand for Valley Nectar Wine), 5 (demand for Valley Red Wine)] is 0
Dual value of resource 1 (grapes) means that if an additional unit of resource 1 (grapes) is available, then the objective value (profit) will increase by 750
Similarly, every additional unit of storage will increase the objective value (profit) by 1200
Similarly interpretation holds for the dual value of all the resources.
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