• 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 following solution 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 of the objective function?
b.	Suppose the unit cost of x1 is decreased to $4. Is the above solution still optimal? What is the value of the objective function when this unit cost is decreased to $4?
c.	How much can the unit cost of x2 be decreased without concern for the optimal solution changing?
d.	If simultaneously the cost of x1 was raised to $7.5 and the cost 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?