OPTIMAL SOLUTION Objective Function Value 20 000 Variable Value Reduced Cost X1 2 400 0 000 X2 3 200 0 000 Constraint Slack Surplus Dual Price 1 0 000 1 000 2 0 000 1 000 3 0 600 0 000 OBJECTIVE COEFFICIENT RANGES The lower limit is how low the coefficient of the variable can go and the upper limit is how high it can go without changing the value of the variables x1 and x2 Variable Lower Limit Current Value Upper Limit X1 1 333 3 000 8 000 X2 1 500 4 000 9 000 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit 1 9 000 12 000 24 000 2 4 000 8 000 9 000 3 2 400 3 000 No Upper Limit a What is the optimal solution (the value of the variables) and the total value of the objective function b Suppose we increase the right hand side of constraint 1 by 2, what is the new value of the objective function c What is the range of optimality for the coefficient of x2 d What constraints are considered binding

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Question: OPTIMAL SOLUTION Objective Function Value = 20.000 Variable Value Reduced Cost X1 2.400 0.000 X2 3.200 0.000 Constraint Slack/Surplus Dual Price 1 0.000 1.000 2

OPTIMAL SOLUTION Objective Function Value = 20.000

Variable	Value	Reduced Cost
X1	2.400	0.000
X2	3.200	0.000

Constraint	Slack/Surplus	Dual Price
1	0.000	1.000
2	0.000	1.000
3	0.600	0.000

OBJECTIVE COEFFICIENT RANGES The lower limit is how low the coefficient of the variable can go and the upper limit is how high it can go without changing the value of the variables x1 and x2.

Variable	Lower Limit	Current Value	Upper Limit
X1	1.333	3.000	8.000
X2	1.500	4.000	9.000

RIGHT HAND SIDE RANGES

Constraint	Lower Limit	Current Value	Upper Limit
1	9.000	12.000	24.000
2	4.000	8.000	9.000
3	2.400	3.000	No Upper Limit

a. What is the optimal solution (the value of the variables) and the total value of the objective function?

b. Suppose we increase the right-hand side of constraint #1 by +2, what is the new value of the objective function?

c. What is the range of optimality for the coefficient of x2?

d. What constraints are considered binding?

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