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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