Assignment 1 (10 marks)
Due – 11:59pm, 11 August 2025
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 Outdoor Furniture Corporation manufactures two products: benches and picnic tables for use in yards and parks. The firm has two main resources: its carpenters (labour) and a supply of redwood for use in the furniture. During the next production period, 3000 hours of manpower are available under a union agreement. The firm also has a stock of 5000 kilograms of quality redwood. Each bench that Outdoor Furniture produces requires A1 labour hours and B1 kilograms of redwood; each picnic table takes A2 labour hours and B2 kilograms of redwood. A completed bench yield a profit of $25 each, and table a profit of $40 each.
Decide the numbers of benches and tables they should produce to maximize the profit.
(1) Please choose the values ofA1, B1, A2 and B2 yourself arbitrarily from the following ranges: 5 ≤ A1 ≤ 10, 5 ≤ A2 ≤ 10, 8 ≤ B1 ≤ 40, 8 ≤ B2 ≤ 40, and establish the model of the optimization problem (LP with 2 variables). State clearly in words what the decision variables are, what the objective function and the equation/inequality constraints represent.
(2) Obtain the graphical solution using MATLAB. Please ignore the fact that the number of benches and the number of tables should be integers.
(3) Change one of the parameters to cause the optimal solution (optimal design variables) changes and solve the problem again.
Question 2:
A cylindrical coordinate robot is to be used for palletizing a rectangular area. Find the maximum rectangular area available within the annular foot-print of the robot workspace. Take r1=A mm and r2= B mm.
(1) Please choose the values ofA and B yourself arbitrarily within the range 200 ≤ A < B ≤ 1000, and develop the mathematical model of the optimisation problem.
(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.