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:

Assume the prediction equation is yi  = c0 + c1x1i + c2 x2i , where c1 , c2 are the prediction

parameters on the quantity of products A and B sold, respectively, and c0 is the intercept. Define x1i , x2i  as the observations on the quantity of products A and B sold, th  respectively, and yi as the observed price. i identifies the i 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)

1)  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)

2)   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)

1)    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:

the formed LP problem using the MATLAB function-linprog.  and solve

(reference: https://en.wikipedia.org/wiki/Linear-fractional_programming)