Q$1)$ Remember the Stickley Furniture$$s problem from Recitation $8($Its LP formulation is provided below$).$

max $=3601+1252+3003$

s$.$t$.$

$801+402+503<=8100()$

$301+202+303<=4500()$

$801+102+503<=9000()$

$1,2,3>=0$

In Recitation $8$ Q$1-$a$,$ the optimal solution was found as $($

$=(20,0,130)$ & $$

$=$ $$46,200).$

a$)$ Find the dual optimal solution using Dual Theorem $($Strong Duality$)$ & Complementary Slackness

Conditions.

b$)$ Answer its part $($f$)$ problem using the Duality Theory, and find the allowable increase and decrease for

the unit profit of under$-$desk$-$cabinets.