Problem about operation research
Problem by AMPL program
I need to
variable
objective
constriction
for this problem
Make sure should be write variable and objective and constriction for each part
there is two part (a) and (b)
A machine shop makes small-run, precision woodworking tools on the following machines:
• Four Grinders
• Two Drill Presses
• Three Lathes
• One Borer
• One Planer
Each product generates a certain amount of gross profit (defined as the selling price less the cost of raw materials and manufacturing). These quantities, together with the time required from each machine for manufacture (in hours) are given in the table below. A dash indicates that the product does not need that particular machine as part of its manufacturing process.
| Tool Produced |
Gross profit |
Grinder |
Drill Press |
Lathe |
Borer |
Planer |
| Dowelling Jig |
10 |
0.5 |
0.1 |
0.2 |
0.05 |
|
| |
| Square |
6 |
0.7 |
0.2 |
|
0.03 |
|
| |
|
| Kerf Ruler |
8 |
- |
- |
0.8 |
- |
0.01 |
| |
|
|
| Tenon Jig |
4 |
|
0.3 |
- |
0.07 |
- |
| |
|
|
| Saw Aligner |
11 |
0.3 |
|
|
0.1 |
0.05 |
| |
|
| Center Scribe |
9 |
0.2 |
0.6 |
|
|
|
| |
|
|
| Honing Guide |
3 |
0.5 |
|
0.6 |
0.08 |
0.05 |
| |
There are limitations on how many of each tool the manager believes the company can sell in each month. Unfortunately, during the next 6 months (Jan - June), certain machines will have to be taken offline for maintenance. The limit to demand and maintenance schedule can be found in the table below
|
Dowelling Jig |
Square |
Kerf Ruler |
Tenson Jig |
Saw Aligner |
Center scribe |
Horning guide |
Tools Offline |
| January |
500 |
1000 |
300 |
300 |
800 |
200 |
100 |
1 Grinder |
| February |
600 |
500 |
200 |
0 |
400 |
300 |
150 |
2 Lathes |
| March |
300 |
600 |
0 |
0 |
500 |
400 |
100 |
1 Borer |
| April |
200 |
300 |
400 |
500 |
200 |
0 |
100 |
1 Drill Press |
| May |
0 |
100 |
500 |
100 |
1000 |
300 |
0 |
1 Grinder and 1 Drill Press |
| June |
500 |
500 |
100 |
300 |
1100 |
500 |
60 |
1 Planer and 1 Lathe |
It is possible to store up to 110 of any completed tool at any time at a cost of 40c per unit per month. There are no tools in stock at the moment, but management would like to have 50 of each tool on hand at the end of the 6 months. The factory works two 8-hour shifts a day, 6 days a week, 25 days a month.
(a) Formulate a linear program to determine the production schedule that maximizes profit?
(b) Someone has suggested that, instead of having the machine maintenance schedule as it is, could the schedule be rearranged to improve profit? Copy and modify your original model to accom¬modate these changes.