Work through the simplex method (in algebraic form) step by step to solve the following problem. Show all work and provide the solution.

Maximize Z = (xsub1) + 2(xsub2) + 3(xsub3) less than or equal to 15

Subject to:

5(xsub1) + 2(xsub2) + 3(xsub3) less than or equal to 15

xsub1 + 4(xsub2) + 2(xsub3) less than or equal to 12

2(xsub1) + xsub3 less than or equal to 8

and

xsub1 greater than or equal to 0

xsub2 greater than or equal to 0

xsub 3 greater than or equal to 0

**Subject Mathematics Operations Research**