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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Definitions:

Net Pay

The take-home pay an employee receives after deductions such as taxes and retirement contributions.

Federal Income Tax

The annual income of individuals, corporations, trusts, and other legal entities is subject to a tax imposed by the IRS.

FICA Tax Rate

The combined percentage rate for Social Security and Medicare taxes that both employees and employers must pay based on earned income.

Hourly Wage

Compensation based on the number of hours worked, typically paid to employees on an hourly rather than salary basis.