Constraints: 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.
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.
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 Costs
‑‑‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑‑ -‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑
X1 8.000 0.000
X2 0.000 5.000
X3 17.000 0.000
X4 33.000 0.000
Constraint Slack/Surplus Dual Prices
‑‑‑‑‑‑‑‑‑‑‑‑‑ -‑‑‑‑‑‑‑‑‑‑‑-‑‑‑ ‑‑‑‑‑‑‑‑‑‑‑‑‑‑
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 questions.
How many necklaces should be stocked?
17
5
8
33
Solution Summary
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.