Introduction to Quantitative Management
Assignment
The weighting of this assignment is 20% in your nal grade. You are encouraged to
discuss in groups, however, the nal report and computer implementation (LINGO
or EXCEL) must be completed individually. A hard copy of the report must be
submitted on 1:30pm Wednesday 15 May 2019 in the lecture, while the computer
implementation (LINGO or EXCEL) must be submitted through UTSOnline before
1:30pm Wednesday 15 May 2019. No late submission will be accepted. The nal
report should follow the structure suggested below:
1) Title
2) Executive summary: a short description of the problem and summary of your
results
3) Problem description: rewrite the problem according to your understanding
4) Formulation of the problem: clearly describe all assumptions; state decision
variables; establish and explain the objective function; determine all constraints
(restrictions) (50% of total marks).
5) Computer implementation (LINGO or EXCEL) and interpretation of the solu-
tion (what is minimum/maximum, which strategy must be applied to achieve this,
etc. Tables, graphs and screen shots will be helpful.) (50% of total marks).
6) Summary
A cover sheet with detailed instruction is included as the last page of this document.
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Problem O.J. Juice Company sells bags of oranges and cartons of orange juice.
O.J. grades oranges on a scale of 1(poor) to 10(excellent). The average quality of
oranges sold in bags must be at least 6, and the average quality of the oranges used
to produce orange juice must be at least 7.5. The average quality is calculated as
the weighted average of the grades of oranges blended together. For example, the
average quality of blending 2 lb of grade 2 oranges and 5 lb of grade 9 oranges is
2 2 + 9 5
2 + 5
O.J. purchases oranges from many dierent suppliers. Each supplier cannot provide
more than its capacity. The capacity, cost and grade mix of the oranges purchased
from ve suppliers are given as an example in the Table below. For example,
supplier 1 cannot provide more than 2,000 lb of oranges; if O.J. purchase 1,000 lb
oranges from supplier 1, after sorting (separating the oranges according to grade),
50 lb of them will be of grade 3, 200 lb of them will be of grade 6, 500 lb will be
grade 8 and 250 lb will be of grade 10.
Supplier capacity Cost $/lb grade 3(%) grade 6 grade 8 grade 10
1 2000 0.9 5 20 50 25
2 1500 0.8 8 25 50 17
3 2500 0.6 10 30 50 10
4 2000 0.4 30 30 30 10
5 1800 0.3 40 40 20 0
The purchased oranges are transported from suppliers to O.J’s dierent warehouses.
The transportation cost per lb is shown as an example in the Table below
Shipping cost($ per lb)
Warehouse A Warehouse B Warehouse C
supplier1 0.10 0.15 0.05
supplier2 0.25 0.09 0.12
supplier3 0.13 0.12 0.10
The sorting process takes place in O.J’s dierent warehouses at dierent cost rate.
The amount of oranges sorted by each warehouse must be within its capacity.
The sorted oranges are transported to OJ’s plant to produce orange juice and bag
of oranges. The transportation cost is $0.05 per lb. Each lb of orange can yield
0.95 lb of bags of orange at a cost of $0.1, while each lb of orange can yield only
0.6 lb of orange juice at a cost of $0.4. The orange juice can be sold at $3.5 per
lb, and the bag of oranges is sold at $1.5 a pound. O.J.’s plant can process no
more than 30,000 lb of oranges, and must produce at least 3000 lb of bags of or-
anges. Oranges not used must be sent to a recycling centre at the cost of $0.1 per lb.
The detailed data can be found in the Excel le with the name 2019AssignData.xlsx.
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Questions:
1) Find the optimal production and shipping plan for the company to maximise
prot with Linear Programming and LINGO.
2) O.J. is considering the opportunity to build a new plant. What data need to be
collected for the evaluation of this decision?
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37141 Introduction to Quantitative Management
ASSIGNMENT COVER SHEET
Please use BLOCK letters (i.e. CAPITALS ONLY) to ll in all details below.
Please DO NOT submit your assignment in a plastic cover, folder or an envelope.
All attachments must be stapled.
Student name:
Student number:
Date due: 1:30pm Wednesday 15 May 2019
Date submitted:
INSTRUCTIONS TO STUDENTS
This is an individual assessment component of the nal grade of this subject. Stu-
dents must complete the declaration below.
Reports to be submitted:
Cover sheet with signature
hard copy of the report
(must submit in the lec-
ture)
LINGO or EXCEL mod-
els (must submit through
UTSOnline)
DECLARATION
I hereby certify that this assignment is my own work, based on my personal study
and/or research and that I have acknowledged all material and sources used in
the preparation of this assignment. I also certify that the assignment has not
previously been submitted for assessment and that I have not copied in part or
whole or otherwise plagiarised the work of other students or authors.
Signature: Date:
