Maximize:$$

z$=30$x$1+48$x$2$

Subject to:$$

$2$x$1+$x$210$

$4$x$1+6$x$222$

$5$x$1+10$x$228$

x$1,$x$20$

Solve this problem using the tableau simplex method. Answer the following questions, given this final tableau:

What are the shadow prices $($reduced costs$)$ of each resource?

What are the allowable ranges $($range for which the current solution remains optimal$)$ of objective coefficients c$1$ and c$2,$ independently?

What are the allowable ranges of resources one $($b$1),$ two $($b$2),$ and three $($b$3),$ independently?$$

Using AMPL, confirm your solutions to the questions. Conducting sensitivity analysis in AMPL is bound to the solver you are using.$$ You should use the CPLEX solver and invoke sensitivity options in order to get the allowable ranges and other values needed.$$