A small company will be introducing a new line of lightweight bicycle frames to
be made from special aluminum alloy and steel alloy. The frames will be
produced in two models, deluxe and professional. The anticipated unit profits
are currently Sh. 1,000 for a deluxe frame and Sh. 1,500 for a professional
frame. The number of kilogrammes of each alloy needed per frame is
summarized in the table below. A supplier delivers 100 kilogrammes of the
aluminum alloy and 80 kilogrammes of the steel alloy weekly.
Aluminum alloy Steel alloy
Deluxe 2 3
Professional 4 2

Required:
(i) Determine the optimal weekly production schedule (14 marks)
(ii) Within what limits must the unit profits lie for each of the frames for
this solution to remain optimal? (4 marks)
(b) Explain the limitations of the technique you have used to solve part (a) above.
(2 marks)