Thread: Linear Programming help

1. Linear Programming help

Have great difficult getting my head around this LP problem in university. Any help would be greatly appreciated. Have LP solver but can't lay out question

A wooden factory has 4 machines to create different size chairs. The machines operate differently and are of different sizes. The firm has been contracted to produce 3 products, 400 units of product 1, 570 of product 2 and 320 of product 3. Productions times are as follows:

----------Machine
Product -1--2 --3--4
--1-----35-41--34--39
--2-----40-36--32--43 ------(Mins)
--3-----38-37--33--40

Machine 1 is available for 150 hours, machine 2 for 240, machine 3 for 200 and machine 4 for 250. The products have different profits depending on which machine they’re produced on, as follows

------------Machine
Product----1----2---3----4
1-------7.8--7.8--8.2--7.9
2-------6.7--8.9--9.2--6.3 (Profit)
3-------8.4--8.1--9.0--5.8

How many units should be produced on each machine to maximise profit?

2. Pretty difficult to "teach" that here (not a classroom).

Did you Google "linear programming"?

3. Originally Posted by bannana
Have great difficult getting my head around this LP problem in university. Any help would be greatly appreciated. Have LP solver but can't lay out question

A wooden factory has 4 machines to create different size chairs. The machines operate differently and are of different sizes. The firm has been contracted to produce 3 products, 400 units of product 1, 570 of product 2 and 320 of product 3. Productions times are as follows:

----------Machine
Product -1--2 --3--4
--1-----35-41--34--39
--2-----40-36--32--43 ------(Mins)
--3-----38-37--33--40

Machine 1 is available for 150 hours, machine 2 for 240, machine 3 for 200 and machine 4 for 250. The products have different profits depending on which machine they’re produced on, as follows

------------Machine
Product----1----2---3----4
1-------7.8--7.8--8.2--7.9
2-------6.7--8.9--9.2--6.3 (Profit)
3-------8.4--8.1--9.0--5.8

How many units should be produced on each machine to maximise profit?
Let's assume you cannot identify the variables involved. These should be $N_{i,j},\ i=1..3,\ j=1,..4$ where $N_{i,j}$ is the number of chair type $i$ produced on machine $j$. Call these $x_k,\ k=1, .., 12$ if that helps.

Now formulate the constraints and the objective in terms of these variables.

CB