The LP problem whose output follows determines how many necklaces, bracelets, ri
ID: 469905 • Letter: T
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.
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.
By how much will the second marketing restriction be exceeded?
NB: You have to use spreadsheet to solve this problem. Type the answer in the space provided below. In your answer just type the number, without any symbols (like $) or comma (,) etc.
If the answer is just a whole number just type whole number. For example, if you want to answer 8 cars. Just type 8.
If the answer is not a whole number type two digits after the decimal points. For example, if your answer is $345,000.654 type 345000.65.
1) X1+2X2+2X3+2X4<108
2) 3X1+5X2+X4<120
3) X1+X3<25
4) X2+X3+X4>50
Explanation / Answer
In slack/surplus and dual price output table, the slack/surplus for the 4th constraint is zero, this means this constraint is binding constraint and is completely utilized.
Thus, the second marketing restriction is exceeding by zero amount.
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