$($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 entering and exiting variables.

$($C$)$ Use the simplex method to solve the problem.

Maximize $P=32x_1+12x_2$

subject $to4x_1+x_{2}4$

$,x_1+5x_{2}4$

$,x_1,x_{2}0$

$($A$)$ Using slack variables, determine the initial system for the linear programming problem. Use $s_1$ for the first constraint and $s_2$ for the second constraint.

First constraint

Second constraint

Objective function

$x_1,x_2,s_1\frac{,}{b}ar(s_2)0$