Question

The LP problem whose output follows determines how many necklaces, bracelets, rings, and earrings a jewelry store should stock. The objective function measures profit; it is assumed that every piece stocked will be sold.Constraint 1 measures display space in units, constraint 2 measures time to set up the display in minutes. Constraints 3 and 4 are marketing restrictions.

using excel solver:

To what value can the profit on ring increases before the solution would change?

LINEAR PROGRAMMING PROBLEM

MAX 100X1+120X2+150X3+125X4

S.T.

	1)  X1+2X2+2X3+2X4<108
	2)  3X1+5X2+X4<120
	3)  X1+X3<25
	4)  X2+X3+X4>50

OPTIMAL SOLUTION

Objective Function Value = 7475.000

Variable	Value	Reduced Cost
X1	8.000	0.000
X2	0.000	5.000
X3	17.000	0.000
X4	33.000	0.000

Constraint	Slack/Surplus	Dual Price
1	0.000	75.000
2	63.000	0.000
3	0.000	25.000
4	0.000	−25.000

OBJECTIVE COEFFICIENT RANGES

Variable	Lower Limit	Current Value	Upper Limit
X1	87.500	100.000	No Upper Limit
X2	No Lower Limit	120.000	125.000
X3	125.000	150.000	162.500
X4	120.000	125.000	150.000

RIGHT HAND SIDE RANGES

Constraint	Lower Limit	Current Value	Upper Limit
1	100.000	108.000	123.750
2	57.000	120.000	No Upper Limit
3	8.000	25.000	58.000
4	41.500	50.000	54.000

  

Use the output to answer the question.

To what value can the profit on ring increases before the solution would change?

Answer 1

From sensitivity report -

Upper Limit of Ring = 162.50

Profit on ring = 150

Profit on Rings can be increased = 162.50 - 150 = 12.50

Hence, profit on ring can be increases by 12.50 before the solution would change.