Thread: 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.

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 and [tex]x\ge 0[tex], 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 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'.