maxz$=3x_1+2x_2$

$s.t.2x_1+x_{2}100(Finishing$ constraint$)$

$x_1+x_{2}80(Carpentry$ constraint$)$

$x_{1}40$

$x_1,x_{2}0$

$(Demand$ constraint$)$

$x_1=$ number $of$ soldiers produced per week

$x_2=$ number $of$ trains produced per week

Show that if available carpentry hours remain between

$60$ and $100,$ the current basis remains optimal. If between

$60$ and $100$ carpentry hours are available, would Giapetto

still produce $20$ soldiers and $60$ trains?