B324 coursework assignment

Academic year 2009/10

Coursework Title:	Linear programming using Octave
Coursework Due Date:	May 30, 2010
Lecturer:	C Nguyen

COURSEWORK DESCRIPTION

Solve and write answers to all 5 problems. The Octave software package is available to use in the Octave web console. A full description of the various options available to use the linear programming solving function in Octave is available online.

Articles and other external sources must be cited and referenced using the Harvard APA format.

This coursework contributes 50% to the B324 unit mark.

PROBLEM 1

Maximize z = x1 - 2x2 - 3x3 - x4

Such that,

x1 - x2 - 2x3 - x4 ≤ 4

2x1 + x3 - 4x4 ≤ 2

-2x1 + x2 + x4 ≤ 1

x1, x2, x3, x4 ≥ 0

Marking criteria:

Problem in matrix format [3 Marks]
Octave program [4 Marks]
Optimal value and optimal solutions [3 marks]

PROBLEM 2

Minimize z = - 2x2 + x3

Such that,

-x1 - 2x2 ≥ -3

4x1 + x2 + 7x3 ≥ -1

2x1 - 3x2 + x3 ≥ -5

x1, x2, x3 ≥ 0

Marking criteria:

Problem in matrix format [3 Marks]
Octave program [4 Marks]
Optimal value and optimal solutions [3 marks]

PROBLEM 3

Minimize z = c1x1 + c2x2 + c3x3

Such that,

x1 + x2 ≥ 1

x1 + 2x2 ≤ 3

x1, x2, x3 ≥ 0

Find the optimal values and optimal solutions when

c = (-1, 0, 1)

c = (0, 1, 0)

c = (0, 0, -1)

Marking criteria:

Octave program [10 Marks]
Optimal values and optimal solutions [5 marks]
Brief discussion of results [5 marks]

PROBLEM 4

ECE Electronics Ltd sells many consumer electronic products through an online catalogue. The company needs substantial warehouse space for storing its goods. Plans now are being made for leasing warehouse storage space over the next 5 months. The amount of space that will be required in each month is known. However, since these space requirements are quite different, it may be most economical to lease only the amount needed each month on a month by month basis. On the other hand, the additional cost for leasing space for additional months is much less than for the first month, so it may be less expensive to lease the maximum amount needed for the entire 5 months. Another option is the intermediate approach of changing the total amount of space leased (by adding a new lease and/or having an old lease expire) at least once but not every month.

The objective is to minimize the total leasing cost for meeting the space requirements. The space requirement and the leasing costs for the various leasing periods are as follows:

Month	Required space (sq ft)
1	30,000
2	20,000
3	40,000
4	10,000
5	50,000

Leasing duration (months)	Cost per sq ft leased
1	£65
2	£100
3	£135
4	£160
5	£190

Marking criteria:

Problem in matrix format [5 Marks]
Octave program [10 Marks]
Optimal values and optimal solutions [5 marks]
Discussion of results [10 marks]

PROBLEM 5

Select an article from an online publication source that can be formulated as a linear programming model. Setup the problem, formulate the linear programming model and solve using Octave.

Below is a list of suggested sources to look for possible articles:

Marking criteria:

Octave program [10 Marks]
Optimal values and optimal solutions [5 marks]
Discussion of problem, results and potential applications [15 marks]

COURSEWORK SUBMISSION

Students are required to submit their coursework online using the Mosaic website.

Supporting images, e.g. charts and images, may be included in the coursework. Students are not permitted to write their coursework using Microsoft Word or Adobe Acrobat document files. The coursework content (text and images) must be written and displayed directly within the Mosaic coursework submission page for each student.

Coursework may be submitted up until midnight of the due date. The timestamp on the coursework submission page is final.