Hello, khrst4!
I haven't use the Simplex Method in decades.
. . But I can solve it with traditional graphic methods.
From , we are in Quadrant 1.
Graph the line: .
It has intercepts:
Draw the line and shade the region above the line.
Graph the line: .
It has intercepts:
Draw the line and shade the region below the line.
Graph the line: .
It has intercepts:
Draw the line and shade the region above the line. Code:

10 *
*
 *
 *
 *
 *
 *
 *
6 * * *
 * * *::::
 * * *::::::::
 * o::::::::::::
 * *:::::::::::
 * * *::::::::::
3 * * *:::::::::
*  * *::::::::
*  **:::::::
*  o::::::
*  **::::
 *          +          * o  
2  5 6
The shaded region has vertices: .
Test those in the function for minimum