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).

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 $\displaystyle N_{i,j},\ i=1..3,\ j=1,..4$ where $\displaystyle N_{i,j}$ is the number of chair type $\displaystyle i$ produced on machine $\displaystyle j$. Call these $\displaystyle x_k,\ k=1, .., 12$ if that helps.

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

CB