Use the following Management Scientist output to answer the questions. MIN 4X1+5
ID: 3109066 • Letter: U
Question
Use the following Management Scientist output to answer the questions.
MIN 4X1+5X2+6X3
S.T.
Objective Function Value = 400.000
Variable
Value
Reduced Cost
X1
0.000
1.500
X2
80.000
0.000
X3
0.000
1.000
Constraint
Slack/Surplus
Dual (Shadow) Price
1
5.000
0.000
2
40.000
0.000
3
0.000
1.250
OBJECTIVE COEFFICIENT RANGES
Variable
Lower Limit
Current Value
Upper Limit
X1
2.500
4.000
No Upper Limit
X2
0.000
5.000
6.000
X3
5.000
6.000
No Upper Limit
RIGHT HAND SIDE RANGES
Constraint
Lower Limit
Current Value
Upper Limit
1
80.000
85.000
No Upper Limit
2
No Lower Limit
280.000
320.000
3
280.000
320.000
340.000
1) X1+X2+X3<85 2) 3X1+4X2+2X3>280 3) 2X1+4X2+4X3>320Explanation / Answer
a.
The optimal solution is obtained from the table containing variable, values, and reduced cost of X1, X2, and X3. From the table, it is clear that optimal solution of the problem is X1 = 0, X2 = 80, and X3 = 0. Objective function value refers to the value of profit contribution. Hence, the value of profit contribution is 400.000.
b.
Identify the binding constraints from the table containing “right hand side ranges”. The constraints having both lower limit and upper limit would be considered as binding. From the table, it is seen that Constraints 1 does not have upper limit. Similarly, Constraint 2 does not have lower limit. Therefore, both the constraints are not binding.
On the other hand, Constraint 3 has both upper and lower limit values specified. Therefore, Constraint 3 is binding.
c.
Shadow price (Dual price) can be determined using the table containing constraints, slack/surplus, and dual price value. From the table, it is seen that shadow price for Constraint 3 is -1.250.
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