Need some Calculus help?

Question

Reviewing some questions for test prep, and stuck on this one:

Maximize - z = 5x1 + 3x2 + 7x3
Subject to: 4x1 + 3x2 + 2x3 < 60
3x1 + 4x2 + x3 < 24
x1 > 0, x2 > 0, x3 > 0

Please help, I stuck at linear programming!

Answer 1

I'll get you started by making the simplex tableau.

We need to insert slack variables into each of the constraints.
4x1 + 3x2 + 2x3 + s1 = 60
3x1 + 4x2 + x3 + s2 = 24

The objective function can be rewritten as
z - 5x1 - 3x2 - 7x3 = 0

The matrix is
x1__x2__x3__s1__s2__z__b
4___3___2___1___0___0__60
3___4___1___0___1___0__24
-5__-3__-7___0___0___1__0

Your pivot column will be the x3 column because that has the most negative number in the bottom row.
The pivot element in that column will be 1 because it has the smallest ratio.
24/1 = 24
60/2 = 30
24 is smaller than 30.