# Math Help - Big M method help

1. ## Big M method help

I'm reading the textbook and trying to learn the material before the class starts. I'm stuck on the Big M method and it has me confused. The problem I'm currently working on is:

Maximize: Z = 3x + 6y
subject to:
+2x + 2y ≤ 16 (if it's not displaying on your computer, thats a <=)
+1x ≥ 4 (this is a >=)

both x ≥ 0 and y ≥ 0

the first part asks to find the initial objective function using the Big M method, then solve for the objective function you will use for the initial simplex tableau.

The second part of the problem asks to find the optimal value for z using the tableau that is provided.

Thanks.

2. Originally Posted by spoord
I'm reading the textbook and trying to learn the material before the class starts. I'm stuck on the Big M method and it has me confused. The problem I'm currently working on is:

Maximize: Z = 3x + 6y
subject to:
+2x + 2y ≤ 16 (if it's not displaying on your computer, thats a <=)
+1x ≥ 4 (this is a >=)

both x ≥ 0 and y ≥ 0

the first part asks to find the initial objective function using the Big M method, then solve for the objective function you will use for the initial simplex tableau.

The second part of the problem asks to find the optimal value for z using the tableau that is provided.

Thanks.
I have no idea what is meant by the "big M" method but isn't your objective function just what you say- 3x+ 6y?
Also, I am no expert on the simplex method so I would solve it graphically:
2x+ 2y= 16 is the same as x+ y= 8 and its graph is the straight line from (0, 8) to (8, 0). The set of points such that $2x+ 2y\le 16$ and [tex]x\ge 0[tex], $y\ge 0$ is triangle below that line, above y= 0 and to the right of x= 0.
x= 4 is the vertical line through, say, (4, 0) and (4, 1) and $x\ge 4$ is to the right of that. That vertical line intersects the y-axis at (4, 0) and intersect the line x+ y= 8 at (4, 4). The "feasible" region, the region satisfying all inequalities is the triangle with vertices (4, 0), (4, 4), and (8, 0). The "fundamental theorem" of linear programming is that a linear function takes on its maximum and minimum values on a convex polygon at one of the vertices. Just evaluate z= 3x+ 6y at each of (4, 0), (4, 4), and (8, 0) to see which is 'optimum'.