The Dervish Chemical Company operates a small plant. Operating the plant requires two raw materials, A and B, which cost $5 and $8 per litre respectively. The maximum available supply per week is 2,700 litres of A and 2,000 litres of B.
The plant can operate using either of two processes, which have differing contributions and raw materials requirements, as follows.
|
|
Raw materials consumed
|
Contribution
|
|
Process
|
(litres per processing hour)
|
per hour
|
|
|
A B
|
$
|
|
1
|
20 10
|
70
|
|
2
|
30 20
|
60
|
The plant can run for 120 hours a week in total, but for safety reasons, process 2 cannot be operated for more than 80 hours a week.
Formulate a linear programming model, and then solve it, to determine how many hours process 1 should be operated each week and how many hours process 2 should be operated each week.