(a) A company manufactures mountain and racing bikes. Each mountain bike is
sold at Sh. 6.375 and a racing bike is sold at Sh. 9,000. A racing bike requires 6
kilogrammes of aluminium while a mountain bike requires 4 kilogrammes of
aluminium. Aluminium cost Sh. 750 per kilogramme. It costs the company Sh.
375 per hour to assemble each bike (irrespective of model). It takes 1 hour to
assemble a racing bike and 2 hours to assemble a mountain bike. There are
4,800 kilogrammes of aluminium available and a total of 1,600 hours available
for assembly.
Required:
(i) Formulate the linear programming problem. (8 marks)
(ii) Graphically solve the problem formulated in (i) above. (12
marks)
(b) Is it appropriate to use non-graphical linear programming methods to solve the
problem in (a) above? Why? (3
marks)
(c) State some of the simplifying assumptions you have made to solve the problem
in (a) above. (4 marks)