https://file.aiquickdraw.com/mathbot/file/1726515884020sws49zeq.pdf

Solve the problems,make sure you make a table for each step but no need to explain,just solve it artificial variable else use simplex/slack variable. Im artificial variable use M, but for normal slack variables use w1,w2,w3 e.t.c, also add a column for check,which is an addition of all the values in the rows

The uploaded file contains a set of linear programming problems. I'll start by solving problem (g), which is asking for the maximization of \( P = 2x + 6y + 4z \) using the simplex method, subject to:

\[
2x + 5y + 2z \leq 38 \\
4x + 2y + 3z \leq 57 \\
x + 3y + 5z \leq 57 \\
x, y, z \geq 0
\]

I will use slack variables \(w_1\), \(w_2\), and \(w_3\) for each constraint to convert inequalities into equalities, and then solve the problem step by step using the simplex tableau. Let's proceed with the initial setup and solving.

### Problem Setup:

1. **Objective Function**:
   \[
   \text{Maximize } P = 2x + 6y + 4z
   \]
   Standard form: 
   \[
   P - 2x - 6y - 4z = 0
   \]
   
2. **Constraints with Slack Variables**:
   \

Solve the problems, make sure you make a table for each step but no need to explain, just solve it using artificial variable. For artificial variables use M, but for normal slack variables use w1, w2, w3, etc. Also add a column for check, which is an addition of all the values in the rows.

This page details how to solve a linear programming problem using the simplex method with artificial and slack variables. The objective function is to maximize P = 2x + 6y + 4z, subject to constraints with slack variables w1, w2, w3 and artificial variable M. Step-by-step solution is provided with a focus on linear optimization methods.

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