A large sub-contractor machines special parts to order. For one order he has two machines, X and Y available. Unfortunately, the machines perform more effectively on some jobs than
others. Machine Y can do 10 units per hour on contracts from Alpha Ltd., 12 per hour on
components from Beater & Co. and 26 per hour on those from Chester Inc., while Machine X
can produce 16, 9 and 10 units per hour respectively. However, this is complicated by certain
constraints which are:
Maximum number of units per month of units from Alpha, Beater and Chesterare 6,500,4,440
and 8000 permonth respectively. The profit for machine X is RM40 per hour and Y is RM24
per hour. The machines X and Y are restricted to working a maximum of 260 and 350 hours
per month respectively.
The problem is to find how many hours should each machine work to maximise profits. This
is answered by plotting machine Y's hours against machine X's hours using mathematical
models for the three suppliers and then solving these using linear programming,
a) Define the variables
b) Define the constraint
c) Define the objective function