An engineering factory makes seven products (PROD 1 to PROD 7) on the following machines: four grinders, two vertical drills, three horizontal drills, one borer, and one planer.[4] Each product yields a certain contribution to profit (defined as £/unit selling price minus cost of raw materials). These quantities (in £/unit) together with the unit production times (hours) required on each process are given below. A dash indicates that a product does not require a process.
|
PROD |
PROD |
PROD |
PROD |
PROD |
PROD |
PROD |
|
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
|
Contribution to |
10 |
6 |
8 |
4 |
11 |
9 |
3 |
|
profit |
|||||||
|
Grinding |
0.5 |
0.7 |
— |
— |
0.3 |
0.2 |
0.5 |
|
Vertical drilling |
0.1 |
0.2 |
— |
0.3 |
— |
0.6 |
— |
|
Horizontal drilling |
0.2 |
— |
0.8 |
— |
— |
— |
0.6 |
|
Boring |
0.05 |
0.03 |
— |
0.07 |
0.1 |
— |
0.08 |
|
Planing |
— |
— |
0.01 |
— |
0.05 |
— |
0.05 |
In the present month (January) and the five subsequent months certain machines will be down for maintenance. These machines will be:
|
January |
1 grinder |
|
February |
2 horizontal drills |
|
March |
1 borer |
|
April |
1 vertical drill |
|
May |
1 grinder and 1 vertical drill |
|
June |
1 planer and 1 horizontal drill |
There are marketing limitations on each product in each month. These are:
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
|
January |
500 |
1000 |
300 |
300 |
800 |
200 |
100 |
|
February |
600 |
500 |
200 |
0 |
400 |
300 |
150 |
|
March |
300 |
600 |
0 |
0 |
500 |
400 |
100 |
|
April |
200 |
300 |
400 |
500 |
200 |
0 |
100 |
|
May |
0 |
100 |
500 |
100 |
1000 |
300 |
0 |
|
June |
500 |
500 |
100 |
300 |
1100 |
500 |
60 |
It is possible to store up to 100 of each product at a time at a cost of £0.5 per unit per month. There are no stocks at present but it is desired to have a stock of 50 of each type of product at the end of June.
The factory works a 6 day week with two shifts of 8 hours each day.
No sequencing problems need to be considered.
When and what should the factory make in order to maximize the total profit? Recommend any price increases and the value of acquiring any new machines.
N.B. It may be assumed that each month consists of only 24 working days.