Assignment 1 (10 marks) There are two questions in this assignment: Question 1 is an LP problem, Question 2 is an NLP problem. Hint: First establish the mathematical model based on the lecture slides. Then get start with MATLAB. Get familiar with the MATLAB program codes provided, L1_ex1_1_simple.m and L1_ex1_3_simple.m or L1_ex1_1_standard.m and L1_ex1_3_standard.m. The simple version of these two codes do not include how to plot the feasible areas and are therefore more suitable for students who are not very familiar with MATLAB. Try to understand the functions in the programs by using MATLAB online help and reading the necessary document. Then obtain the graphical solutions to the following two questions by making necessary changes to the codes. Please go to the tutorial classes to know more about MATLAB, the modelling, and the detailed requirements. You must complete the MATLAB quiz in Week 0 before submitting Assignment 1, otherwise your assignment will be marked as a 0. Question 1: The local bookstore must determine how many of each of the four new books on photonics it must order to satisfy the new interest generated in the discipline. Book 1 costs $50, will provide a profit of $10, and requires 3 inches of shelf space. Book 2 costs $70, will provide a profit of $12, and requires 8 inches of shelf space. Book 3 costs $80, will provide a profit of $8, and requires 2 inch of shelf space. Book 4 costs $65, will provide a profit of $15, and requires 2 inches of shelf space. Find the number of each type that must be ordered to maximize profit. Total shelf space is 620 inches. Total amount available for ordering is $9500. It has been decided to order at least 20 Book 3. (1) Establish the model of the optimisation problem. State clearly in words what the decision variables are, what the objective function and the equation/inequality constraints represent. (2) Suppose the number of Book 3 is half the number of Book 1, and the number of Book 4 is fixed as 13, establish the model of the new optimisation problem. (3) For the model established in step (2), obtain the graphical solution using MATLAB. (4) Change one of the parameters to cause the optimal solution (optimal design variables) changes and solve the problem again. 1 Question 2: Determine the objective function for building a minimum-cost cylindrical tank of volume 60m3 and the height should be at least 2m longer than the radius, it should be noted that the cylindrical tank does not have a lid. If the circular ends cost $12 per m2 , the cylindrical wall costs $5 per m2 , the reinforcement cost for the base is $20 per m2, and it costs $30 per m2 for the protecting material over the whole surface (double sides). Additionally, the base requires an extra 10% of its total cost for transportation and installation fees. (1) Establish the mathematical model of the optimisation problem. State clearly in words what the decision variables are, what the objective function and the equation/inequality constraints represent. (2) Draw the graphs and find the optimal solution (graphical solution). (3) Change one of the parameters to cause the optimal solution (optimal design variables) changes and solve the problem again. (4) If this tank needs a lid, rebuild the mathematical model and solve the problem again. 2 Assignment 1 Submission Guide · Attempt two questions: one linear programming problem (questions 1) and one non- linear programming problem (questions 2). · Write a short report in PDF document format. Submit the written code separately (MATLAB scripts) for each question you have attempted along with the report. Make sure to name the files with the question number and name the MATLAB script (.m extension file) with your student ID. Submit the files to Canvas TurnItIn using the multiple file upload option. For example, the three files could be: Assignment_1_DOM_13123456.PDF, Qestion_1_DOM_13123456.m and Qestion_2_DOM_13123456.m . File Upload Text Entry Upload a file, or choose a file you've already uploaded. File: Choose file No file chosen PDF report + Add Another File MATLAB scripts (.m file) Click here to find a file you've already uploaded Comments ... Cancel Submit Assignment . No marks will be given if you do not upload the MATLAB scripts along with the report. · The assignment is worth 10 marks, each question is worth 5 marks. · For question1: o For sub-question (1), write the model of the optimisation problem (0.5 marks), describe the decision variables, objective function, and equality/inequality constraints (1 mark) o Solve sub-question (2) (0.5 marks) o For sub-question (3), find the optimal solution by the code of MATLAB and give an image of the graphical solution (2 marks) 3 o For sub-question (4), find the optimal solution and write the values of the design variables, objective function, and equality/inequality constraints (0.5 marks). Given the corresponding code and the image of the graphical solution (0.5 marks) · For question 2: o For sub-question (1), write the model of the optimisation problem (0.5 marks), describe the decision variables, objective function, and equality/inequality constraints (1 mark) o Solve sub-question (2), find the optimal solution by the code of MATLAB and give an image of the graphical solution (1.5 marks) o For sub-question (3), find the optimal solution and write the values of the design variables, objective function, and equality/inequality constraints (0.5 marks). Given the corresponding code and the image of the graphical solution (0.5 marks) o If this tank needs a lid, rebuild the mathematical model (0.5 marks) and solve the problem again (0.5 marks). · Include the code with proper comments in line to explain each code line that you have written to solve each question and attach it with the report. . For clarity, we might ask you to explain what you have written and how the code works. No mark will be given if you cannot explain the results and the code. . Any suspicious plagiarism will be reported to the university for further investigation. And the mark will not be given until the investigation is finished. . As stated in the subject outline, "Work submitted late without an approved extension is subject to a late penalty of 10 per cent of the total available marks deducted per calendar day that the assessment is overdue (e.g. if an assignment is out of 40 marks, and is submitted (up to) 24 hours after the deadline without an extension, the student will have four marks deducted from their awarded mark). Work submitted after five calendar days is not accepted and a mark of zero is awarded". 4