## Simplex Method - Big M problem

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### Simplex Method - Big M problem

Hey everyone. I cant figure out how to set this word problem up for the simplex Big M method. Any help would be greatly appreciated!

A company produces two types of mixes, Mix R and Mix D

Mix R has at least 20% nuts
Mix R has at most 40% Bolts

Mix D has at least 30% nuts
Mix D has at most 40% bolts.

The company has available to it:

1200 pounds of screws
750 pounds of nuts
1500 pounds of bolts

Knowing that the company makes \$0.60 dollars per pound of mix D and \$0.40 dollars per pound of mix R how many pounds of nuts, bolts and scews should be used to maximise the companies profit.
Abomz

Posts: 4
Joined: Sun Mar 23, 2014 4:40 pm

### Re: Simplex Method - Big M problem

Abomz wrote:A company produces two types of mixes, Mix R and Mix D

Mix R has at least 20% nuts
Mix R has at most 40% Bolts

Mix D has at least 30% nuts
Mix D has at most 40% bolts.

The company has available to it:

1200 pounds of screws
750 pounds of nuts
1500 pounds of bolts

Knowing that the company makes \$0.60 dollars per pound of mix D and \$0.40 dollars per pound of mix R how many pounds of nuts, bolts and scews should be used to maximise the companies profit.

The artificial variables will likely be used to account for the "at least" and the "at most". How far have you gotten so far? What variables are you using, and what constraints have you developed thus far?

Note: You should be able to check your eventual answer in calculators such as this one.
nona.m.nona

Posts: 255
Joined: Sun Dec 14, 2008 11:07 pm

### Re: Simplex Method - Big M problem

Thanks for engagin nona.m.nona

Heres what ive come up with so far:

Let

x = amount of nuts in mix R
y = amount of bolts in mix R
z = amout of screws in mix R

p = amount of nuts in mix D
q = amount of bolts in mix D
r = amount of screws in mix D

Maximise P where:
P = 0.4 (x + y + z) + 0.6 (p + q +r )
Where:
x + p <= 750
y + q <= 1500
z+ r <= 1200

Where I am getting stuck is incorporating the ingrediants into inequalities.

Mix R has at least 20% nuts
Mix R has at most 40% Bolts

and

Mix D has at least 30% nuts
Mix D has at most 40% bolts

I cant figure out how to make these work for equaitons that can go into the simplex method.
Abomz

Posts: 4
Joined: Sun Mar 23, 2014 4:40 pm