OK, I didn't complete it for you.
I only had a half hour to learn anything about it, but I thought it might still be fun to try it anyway. I could only get halfway through without having a calculator available. But this show the steps toward solving it, you can do the rest to complete it.
I've never even heard of standard maximization problems before and so I didn't have time to learn it enough to solve it completely.
I did the best I could to format a table with characters available. LOL. Since the editor strips out spaces I used dots to space everything out. Just ignore the dots as though they are whitespace.
I know it isn't a complete solution, but maybe it can get you started if you understand it at all. The first steps of solving this up till the point of making the first calculations in the calculator are here:
Maximize: z = 12x1 + 15x2 + 10x3
............. -12x1 - 5x2 -10x3 + z = 0
subject to:
2x1 + 2x2 + x3 s1 ...=< 8 ........\ 2 slack variables
x1 + 4x2 + 3x3 ... s2=< 12 ....../
x1, x2, x3 >= 0 ....................... 3 variables, 3 non basic variables
_...x1...x2...x3...s1...s2...z.|......_
|....2....2....1....1....0....0..|...8..| 8/2=4 smaller non neg entry
|....1....4....3....0....1....0..|.12..| 12/1=12
|--------------------------|----|
|.-12..-5..-10...0....0....1...|..0...|
--.^...............................|.....--
....^most neg indicator
....^pivot on the 2
..1/2 R1 -> R1 ........... *row(1/2,[A],1) -> [A]
.-1 R1 + R2 -> R2 ...... *row(-1,[A],1,2) -> [A]
.12 R1 + R3 -> R3 ...... *row(12,[A],1,3) -> [A]
If I had a calculator or knew how to perform the calculations by hand I could have completed this for you. Just perform the calculations and then you should get the next tableau, and you can continue maximizing till you solve it.
If you can't find the complete solution, hopefully this first half of the problem can get you started so you can complete it yourself.
Good Luck.
