QUESTION
University of Ballarat
School of Science, Information Technology & Engineering
ENCOR2031 Fundamentals of Engineering (Applied Math 2)
Semester 1, 2012
Assignment 3 (20 marks)
1.Set up and solve graphically the following optimization problem. [Carefully define
all variables used and explain how you obtained the objective function and the
constraints, graph neatly, do any calculations required to obtain an exact solution,
and report your results in the context of the situation.
Acme Computer Supplies produces two home computer products: a laptop computer
and a desktop computer. They both use the same CPU, and ACS can only get 120
CPUs each week. This is unfortunate as ACS has an effective sales team, and can
sell as many computers as it can produce. Each desktop produces a profit of $120,
and each of the desirable laptops can be sold for a profit of $180.
Apart from the limitation in CPU supply, the other factors ACS has to consider are
assembly time and program installation time. ACS has ten hardware technicians who
assemble all the computers. They each work forty hours per week and take four
hours to assemble each laptop and two hours to assemble each desktop. ACS also
has eight software technicians who install the bundled software. They also work forty
hours per week and take an hour to deal with each laptop. The desktops are to be
sold with a very comprehensive suite of programs, so each one takes three hours
installation time.
(a) How many of each computer should ACS produce per week, in order to maximize
its profit? (There may not be enough work to keep all the technicians busy all the
time.)
(b) The sales team believes that after an innovative advertising campaign focusing
on the extensive software provided with the desktop computers, it will be possible to
increase their price so that $200 profit is gained from each sale. In that case, what
should the production schedule be?
2.Find eigenvalues and eigenvectors of:
�
0 0 2
0 2 0
2 0 0
�
[3 marks]
[4 marks]
3. Solve the system:
