3. Consider the following linear program: MIN 6x1 + 9x2 ($ cost) s.t. x1 +2x2 ?8 10x1 + 7.5x2...

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General Management

3. Consider the following linear program:
MIN 6x₁ + 9x₂ ($cost)
s.t. x₁ +2x₂ ?8
10x₁ + 7.5x₂ ? 30
x₂ ? 2
x₁,x₂ ?0
The Management Scientist provided the followingsolution output:
OPTIMAL SOLUTION
Objective Function Value = 27.000
Variable
Value
Reduced Cost
X1
1.500
0.000
X2
2.000
0.000
Constraint
Slack/Surplus
Dual Price
1
2.500
0.000
2
0.000
?0.600
3
0.000
?4.500
OBJECTIVE COEFFICIENT RANGES
Variable
Lower Limit
Current Value
Upper Limit
X1
0.000
6.000
12.000
X2
4.500
9.000
No Upper Limit
RIGHT HAND SIDE RANGES
Constraint
Lower Limit
Current Value
Upper Limit
1
5.500
8.000
No Upper Limit
2
15.000
30.000
55.000
3
0.000
2.000
4.000
A. What is the optimal solution including the optimal value ofthe objective function?
B .Suppose the unit cost of x1 is decreased to $4. Isthe above solution still optimal? What is
the value of the objective function when this unit cost isdecreased to $4?
C. How much can the unit cost of x2 be decreasedwithout concern for the optimal solution
changing?
D. If simultaneously the cost of x1 was raised to $7.5 and thecost of x2 was reduced to $6,
would the current solution still remain optimal?
E. If the right-hand side of constraint 3 is increased by 1,what will be the effect on the
optimal solution?

Answer & Explanation Solved by verified expert

4.2 Ratings (659 Votes)

A The optimal solution is X1 15 and X2 2 This makes the objective function value as 615 92 27 It is found in the variable table and their corresponding values B Yes The third table objective coefficient range shows that the lower limit for X1 is 0 The See Answer

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Constraint	Slack/Surplus	Dual Price
1	2.500	0.000
2	0.000	?0.600
3	0.000	?4.500

Variable	Lower Limit	Current Value	Upper Limit
X1	0.000	6.000	12.000
X2	4.500	9.000	No Upper Limit