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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.