Refer to the model listed next:

Max: $Z={10}^{**}x1+6^{**}2+4^{**}x3$;

Subject to:

$x1+x2+x3100$; $(technical)$

${10}^{**}1+4^{**}2+5^{**}3600$; $(labor)$

$2^{**}1+2^{**}2+6^{**}3=300$; $(administration)$

$x1,x2,x30$; where $x1,x2$ and $x3$ are the number of product $1,2$ and $3$ produced.

$($i$)$ Identify the initial basis with your reason.

$($ii$)$ Show one complete iteration as the solution moves to the next basis.

$($iii$)$ Find the optimal basis. You may solve the problem for the optimal solution using the Lingo software but must validate the optimal basis.

$($iv$)$ Estimate the optimal simplex multipliers.

$($v$)$ Solve the model using the Lingo software and report the dual prices for each constraint.

$($vi$)$ Compare the optimal simplex multipliers with the shadow prices for different constraints and provide your comments.