Linear Programming

[Delta88]

A furniture warehouse sells 2 types of furniture, flix and flox.

The maximum sales of flix are 5500, and 3,500 flox.

x= the number of flix
y= the number of flox

The objective function is C=24x + 20y

Direct Labour:The supply of grade A labour is restricted to 9,000 hour but is

freeley avaliable for grade B labour.

Machine time: The hours avaliable for macine type 1 are 5000, and 8000 for

machine type 2.

Flix require 2hrs of grade A labour, 1 hr of B labour, a hour of machine 1 and

1 hour of macinhe 2.

Flox require 1.5hrs Grade A, 2hrs Grade B, 1 hr machine type 1, and 2 hours

machine type 2/

So I set up the linear programme:

Maximise profits for: P= 24x + 20y
Subject to:
2x+1.5y <= 9000
1x+2y >=0
1x+2y <= 5000
1x + 2y <=8000

x,y >= 0

Then solve using the simplex algorithm

But when I solve using a simplex algorithm I find that x and y =0 which cant be right, because you need to sell something to make profit. I was wondering wether I set the linear program up wrong.

[Logophobic]

I don't know anything about linear programming or simplex algorithms, but:
Flox require 1.5hrs Grade A, 2hrs Grade B, 1 hr machine type 1, and 2 hours machine type 2/

1x+2y <= 5000

Shouldn't that eq be x+y<=5000?

[Rassis]

Objective function: max.Z = 24X + 20Y

Constraints:

Grade A: 2X + 1.5Y <= 9,000
Grade B: X + 2Y >= 0
Type 1: X + Y <= 5,000
Type 2: X + 2Y <= 8,000
0 <= X <= 5,500
0 <= Y <= 3,500

Solution: X = 3,000 units; Y = 2,000 units; Income = 112,000 €

Regards,

[Delta88]

Did you do that by simplex algorithm cause if you did could you possibly shown me how you got that

[Rassis]

I am sorry but the simplex algorithm is boring and too much time consuming. I left it apart since long. In my professional activities, I use Solver in Excel or What´s Best, Lingo or Lindo software instead. But this is not a choice if you are still a student, of course…

If you want, I can attach the solution obtained in Excel.

[Delta88]

Yeah that would be good thank you

[Rassis]

Here it is. Have a good time.

[Delta88]

am very confused now casue when I am doing the simplex alogrithm I get this which I dont think it right , cause its not what you got:

p= £62000
x= 0
y=4000

Would anybody be willing to post a simplex algorithm

by the way have just tried this programme at the following link:

http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/simplex.html

and it got this:

Optimal Solution: p = 108800; x = 4200, y = 400

Tableau #1
x y s1 s2 s3 s4 p
2 3/2 1 0 0 0 0 9000
1 2 0 -1 0 0 0 0
1 2 0 0 1 0 0 5000
1 2 0 0 0 1 0 8000
-24 -20 0 0 0 0 1 0

Tableau #2
x y s1 s2 s3 s4 p
1 3/4 1/2 0 0 0 0 4500
0 -5/4 1/2 1 0 0 0 4500
0 5/4 -1/2 0 1 0 0 500
0 5/4 -1/2 0 0 1 0 3500
0 -2 12 0 0 0 1 108000

Tableau #3
x y s1 s2 s3 s4 p
1 0 4/5 0 -3/5 0 0 4200
0 0 0 1 1 0 0 5000
0 1 -2/5 0 4/5 0 0 400
0 0 0 0 -1 1 0 3000
0 0 56/5 0 8/5 0 1 108800

So maybe the answer i had before was wrong

[Rassis]

I used your link. I entered:

Maximize p = 24x + 20y subject to
2x + 1.5y <= 9000
x + y <= 5000
x + 2y <= 8000
x <= 5500
y <= 3500

And got the answer: Optimal Solution: p = 112000; x = 3000, y = 2000

Maybe you haven´t entered the data correctly.

[Delta88]

Yeah I think I might have thank you

[DomoCobra]

Ah I hated simplex in maths boring monotoneous(sp) hours of simplex :(