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namereport.pdf: A pdf file created in any word processor
containing the solutions of the questions, appropriate graphs,
tables and references. The file should be labelled with your name.
This file should consist of up to pages, pages with title page
namecode.R: Two codes combined in one R file, labelled
with yourname.R with codes for the LP models for Question
and Question
Your assignment wiA garment factory produces shirts and pants for Kmart chain. The contract is such that
quality control is done before shipping and all products supplied to Kmart satisfying the
quality requirements would be accepted by the chain. The factory employs workers
in the cutting department, workers in the sewing department, and workers in the
packaging department. The garment factory works productive hours a day no idle
time during these hours There is a daily demand for at most shirts. The demand
for pants is unlimited. Each worker can participate only in one activity the activity to
which they are assigned. The table below gives the time requirements in minutes and
profit per unit for the two garments.
Amount minutes per operation
Cutting Sewing Packaging Profit per unit$
Shirts
Pants
a Explain why a Linear Programming LP model would be suitable for this case study.
marks
b Formulate a LP model to help the factory management to determine the optimal daily
production schedule that maximises the profit while satisfying all constraints.
marks
c Use the graphical method to find the optimal solution. Show the feasible region and
the optimal solution on the graph. Annotate all lines on your graph. What is the optimal
daily profit for the factory?
marks
Note: you can use graphical solvers available online but make sure that your graph is
clear, all variables involved are clearly represented and annotated, and each line is clearly
marked and related to the corresponding equation.
d Find the range for the profit $ per shirt if any that can be obtained without affecting the optimal point of part c
marks
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