(Solved): A.B.C.part A. B. C is all together.  (A) Using slack variables, determine the initial system fo ...

(A) Using slack variables, determine the initial system for the linear programming problem. (B) Write the simplex tableau and identify the first pivot and the entoring and exiting variables: (C) Use the simplex method to solve the problem Maximize \( \quad P=18 x_{1}+x_{2} \) \( 2 x_{1}+x_{2} \leq 12 \) \( x_{1}+8 x_{2} \leq 12 \) \( x_{1}, x_{2} \geq 0 \) (A) Using slack variables, determine the initial bystem for the linear progranming problem. Use \( s_{1} \) for the first constraint and s for the second constraint. First constraint Second constraint Objective function The pivot element is located in the \( \square \bar{\nabla} \) column and \( \bar{\nabla} \) row. The entering variable is The exiting variable is (C) Use the simplex method to solve the problem. Select the correct thoice below and, if necessary, fill in the answer boxes to complete your choice A. The maximum value is \( P= \) when \( x_{1}=\quad \) and \( x_{2}= \) (Type integers of simplified fractions) B. There is no optimal solution