For this assignment, you are required to carry out the process of attempting to solve
different optimisation problems. For each question, you are required to report your
results in detail. It should include your best solution and its corresponding solution
procedures. If you are asked to solve those sub-questions using MATLAB, then their
MATLAB source code is required.
Marks will be awarded based on how well your submission addresses the above
points.

Question 1
You have certain types of chicken wire to build a temporary enclosure for holding
chicken at your backyard. You plan to build a triangular enclosure (the lengths of
three sides are x, y and z, respectively. See Figure 1)

Figure 1 Triangular enclosure (chicken house)

You have 100m of Type-1 chicken wire, and you want to maximise the area of the
enclosure for your given materials.

– If z=18, please find the lengths of two sides x, y using the Lagrange
multiplier method. (Note: you are asked to consider a two-dimensional
(2D) optimisation procedure.)
x
y
z
2
(15 marks)

– If the lengths of two sides have the following relationship: x=y. Please find the
lengths of three sides x, y, z using the Successive Parabolic Interpolation
method and Newton’s method. Please convert it to be a one-dimensional
optimisation problem and provide your matlab code.