A company manufactures four products (1, 2, 3, 4) on two machines (X and Y).
The time to process one unit of each product on each machine is shown
below:
Product Machine X (minutes) Machine Y (minutes)
1 10 27
2 12 19
3 13 33
4 8 23
The profit per unit for each product is shown as below:
Product 1=$10 Product 2=$12 Product 3=$16 Product 4=$5
Product 1 must be produced on both machines X and Y but products 2, 3, and
4 can be produced on either machine.
The factory’s floor space is very limited. Only one week’s production is stored
in 50m2 floor space where the floor space taken up by each product is 0.1m2,
0.15m2, 0.5m2 and 0.05m2 for products 1, 2, 3 and 4 respectively.
Customer requirements mean that the amount of product 3 produced should
be related to the amount of product 2 produced – twice as many units of
product 2 should be produced as product 3 over a week.
Machine X is out of service for maintenance or breakdown 5% of the time and
machine Y 6% of the time.
Assume a working week for 40 hours, formulate the problem of how to
manufacture these product with aim to maximize company’s profit.