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  3. Linear Programming
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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

&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209; &#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209; -&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;

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

&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209; -&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;-&#8209;&#8209;&#8209; &#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;

1 0.000 75.000

2 63.000 0.000

3 0.000 25.000

4 0.000 &#8209;25.000

OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper Limit

&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209; &#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209; &#8209;&#8209;&#8209;--&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209; &#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;

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

&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209; &#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209; &#8209;&#8209;--&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209; &#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;&#8209;

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.

$2.19