Assignment 1: Optimisation

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Assignment 1: Optimisation
Due date: 30 August 2019 12:00
Where to submit: Submit the assignment report via the Blackboard turnitin
assignment submission system.
This assignment is worth 20% of the total marks for the course.
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 details. 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 2
Suppose a linear equation is to be fit predicting raw material price as a linear
function of the quantity of product A and produce B (made of the same raw material)
sold given the following data:
Table 1
Quantity of product A sold Quantity of product B sold Price of raw material
9 1 5
13 8 2
17 3 9
8 5 10
10 9 4
15 2 6
Assume the prediction equation is , where are the prediction
parameters on the quantity of products A and B sold, respectively, and is the
intercept. Define as the observations on the quantity of products A and B sold,
respectively, and as the observed price. identifies the observation.
1) Suppose the desired criterion for equation fit is that the fitted data exhibit
minimum of the sum of the absolute deviations between the raw material price
and its prediction.
Please develop a LP model to minimize the sum of the absolute deviations solve
the formed LP problem using the MATLAB function-linprog.
(20 marks)
i ii 0 11 2 2 y c cx cx =+ + 1 2 c c,
0 c
1 2 ,i i x x
i y i th i
2
2) Suppose the desired criterion for equation fit is that the fitted data exhibit minimum
of the largest absolute deviation between the raw material price and its prediction.
Please develop a LP model to minimise the largest absolute deviation and write
down the tabular form of the formed LP problem.
(20 marks)
3) Suppose the desired criteria for equation fit is that the fitted data exhibit minimum
sum of the squared deviations between the raw material price and its prediction. You
are then asked to solve the formed least square (LS) problem.
– Write down the linear system equation (Ax=B) of the LS problem, and solve it
using the normal equations approach.
(10 marks)
4) Assume we have two additional groups of datasets similar to Table 1, and for
each dataset, we have found out their predictions
�” = 10 + 18�” + 17�*,
�* = 100 + 40�” + 41�*,
Where �”, �* (products A and B) are both positive variables and subject to the
following constraints:
15�” + 10�* ≤ 60
30�” + 40�* ≤ 200
– Please develop a LP model to maximise the ratio � = “45”6785″97:
“445;4785;”7:
and solve
the formed LP problem using the MATLAB function-linprog.
(reference: https://en.wikipedia.org/wiki/Linear-fractional_programming)
(5 marks)

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