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. Constraints measure display space in units, time to set up the display in minutes and two marketing restrictions.

MAX 100N+120B+150R+125E

N+2B+2R+2E <108 Space 3N+5B+ E <120 Time

N+ R <25 market restriction 1 b+r+ e>50 Market Restriction 2

OPTIMAL SOLUTION

Objective Function Value = 7475.000

Variable Value Reduced Costs

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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

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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

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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

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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 solve and answer the following question. By how much will marketing restriction 1 be exceeded?