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COMP4130-E4
A Level 4 Module Autumn 2024/2025
Linear and Discrete Optimization
Instructions:
Time allowed: FOUR Weeks Complete ALL THREE Tasks
For this coursework, you shall use the Excel and LP-Solve software to solve the Farm Management linear programming problem, including three tasks. After completing the coursework, you need to submit your solutions in a ZIP package through the Moodle system, named by “COMP4130-CW-Solutions-NAME-ID.zip” with “NAME” and “ID” replaced by your name and student ID respectively. The ZIP package should include the following files:
1 Three Excel files for the spreadsheet models of three tasks. Please name the files for the three tasks respectively as “COMP4130-CW-Task1-ID.xlsx”, “COMP4130- CW-Task2-ID.xlsx”, and “COMP4130-CW-Task3-ID.xlsx”, by replacing “ID” with your own 8-digit student ID. All the Excel files should annotate the parameter data, decision variables, intermediate variables and objective variables.
2 Three LP-Solve files for the algebraic models of three tasks. Please name the files for the three tasks respectively as “COMP4130-CW-Task1-ID.lp”, “COMP4130-CW- Task2-ID.lp”, and “COMP4130-CW-Task3-ID.lp”, by replacing “ID” with your own 8-digit student ID. All the lp files should have the comments on the constraints and optimization objectives.
In addition, you need to submit a PDF report to explain your problem modelling and solving processes for the three tasks. Before the submission of your report, you need to complete the coursework submission coversheet on the Moodle page and attach the screenshot of the competion as the first page of your report. The report requires to use font 12pt and not exceed 10 pages. In your report, for each task, you should identify the data, decision variables, objective function and constraints, write the algebraic expressions of the objective function and constraints, and explain how to implement your formulated objective function and constrains in Excel Spreadsheet and LP-Solve, show the screenshots of the optimization results produced by Excel Spreadsheet and LP-Solve, check the consistency between the results of the two types of software.
Please name the report as “COMP4130-CW-Report-NAME-ID.pdf”, by replacing “NAME” with your name and “ID” with your 8-digit student ID.
Permitted resources:
Those whose first language is not English may use a standard translation dictionary to translate between that language and English provided that neither language is the subject of this examination.
The coursework is open-book. You are free to refer to the textbook, lecture notes and workshop sample solutions for solving the linear programming problem.
Prohibited resources:
ChatGPT and other AI language tools are not allowed to be used for report writing.
Appended material: NONE
Additional material: NONE
Information for Invigilators: NONE
1. Farm Management Problem. Fred Jonasson manages a family-owned farm. To supplement several food products grown on the farm, Fred also raises pigs for mar- ket. He now wishes to determine the quantities of the available types of feeds (corn, tankage, and alfalfa) that should be given to pigs. Since pigs will eat any mix of these feed types, the objective is to determine which mix will meet certain nutri- tional requirements at a minimum cost. The number of units of each type of basic nutritional ingredient contained within a kilogram of each feed type is given in the following table, along with the nutritional requirements and feed costs:
|
Nutritional Ingredient |
A Kilogram of Corn |
A Kilogram of Tankage |
A Kilogram of Alfalfa |
Minimum Requirement |
|
Carbohydrates |
90 |
20 |
40 |
200 |
|
Protein |
30 |
80 |
60 |
180 |
|
Vitamins |
10 |
20 |
60 |
150 |
|
Cost |
$10.50 |
$9.00 |
$7.50 |
|
(a) Develop an Excel spreadsheet model (with file name “COMP4130-CW-Task1- ID.xlsx”) and an LP-Solve model (with file name “COMP4130-CW-Task1-ID.lp”) to solve the basic Farm Management Problem. Document a report for this task in file “COMP4130-CW-Report-NAME-ID.pdf”. (40 marks)
(b) Based on the basic model built by Task 1, by making some necessary changes on the problem formulation, develop an Excel spreadsheet model (with file name “COMP4130-CW-Task2-ID.xlsx”) and an LP-Solve model (with file name “COMP4130-CW-Task2-ID.lp”) to solve the Farm Management Problem, with the additional condition:
Fred Jonasson wants to maintain the relative balance on the consumption of the three feed types. He decides to restrict the quantity difference of any two consumed feed types not exceeding ( ≤) 0.5 kilogram.
Document a report for this task in file “COMP4130-CW-Report-NAME-ID.pdf”. (15 marks)
(c) Based on the basic model built by Task 1, by making some necessary changes on the problem formulation, develop an Excel spreadsheet model (with file name “COMP4130-CW-Task3-ID.xlsx”) and an LP-Solve model (with file name “COMP4130-CW-Task3-ID.lp”) to solve the Farm Management Problem, un- der the following scenario:
Before determining the best mix of the three feed types, Fred Jonasson has already packed the feeds into bags, with each bag weighting 0.25 kilogram. To reduce the feed dispensing workload, Fred Jonasson decides to allocate the three types of feeds to pigs in bags. Please help Fred Jonasson deter- mine how many bags of the three types of feeds should be given to pigs with the minimum cost but satisfying the nutritional ingredient requirements.
Document a report for this task in file “COMP4130-CW-Report-NAME-ID.pdf”. (15 marks)