Linear Programming

[e. cools]

Hello,

I have the following linear programming question:
Company 1:
maximize: z=3x1+4x2+6x3+x4
subject to:
x1+x2 <= 500
x3+x4 <= 50
x1+x3 <= 100
x2+x4 <= 150

Company 2:
maximize: z=3x1+4x2+6x3+x4
subject to:
x1+x2 <= 100
x3+x4 <= 500
x1+x3 <= 50
x2+x4 <= 150

The companies want to work together.
what is the new LP model of the two companies working together?
I have the following sollutions, but I can't figure out which one to take. I should say the second option because then the profits are higher for both companies.

1.
Company 1&2
maximize: z=3x1+4x2+6x3+x4
subject to:
2x1+2x2 <= 600
2x3+2x4 <= 550
2x1+2x3 <= 150
2x2+2x4 <= 300
or
maximize: z=6x1+8x2+12x3+2x4
subject to:
2x1+2x2 <= 600
2x3+2x4 <= 550
2x1+2x3 <= 150
2x2+2x4 <= 300

Thank you for helping me out on this!

[emmanuel moemeke]

i want a write up on lenear programing