The LP Problem Whose Output Follows Determines How Many Necklaces,bracelets,rings,and

question 45

Essay

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 $$\begin{array} { c r c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { X1 } & 8.000 & 0.000 \\\text { X2 } & 0.000 & 5.000 \\\text { X3 } & 17.000 & 0.000 \\\text { X4 } & 33.000 & 0.000\end{array}$$ $$\begin{array} { c c r } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\\hline1& 0.000 & 75.000 \\2 & 63.000 & 0.000 \\3 & 0.000 & 25.000 \\4 & 0.000 & - 25.000\end{array}$$ OBJECTIVE COEFFICIENT RANGES $$\begin{array} { c c c c } \text { Variable } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\\text { X1 } & 87.500 & 100.000 & \text { No Upper Limit } \\\text { X2 } & \text { No Lower Limit } & 120.000 & 125.000 \\\text { X3 } & 125.000 & 150.000 & 162.500 \\\text { X4 } & 120.000 & 125.000 & 150.000\end{array}$$ RIGHT HAND SIDE RANGES $$\begin{array} { c c c c } \text { Constraint } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\1 & 100.000 & 108.000 & 123.750 \\2 & 57.000 & 120.000 & \text { No Upper Limit } \\3 & 8.000 & 25.000 & 58.000 \\4 & 41.500 & 50.000 & 54.000\end{array}$$ Use the output to answer the questions.
a.How many necklaces should be stocked?
b.Now many bracelets should be stocked?
c.How many rings should be stocked?
d.How many earrings should be stocked?
e.How much space will be left unused?f. How much time will be used?g. By how much will the second marketing restriction be exceeded?

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