Luis has a choice between working for $$6$ per hour, or not working at all. If Luis chooses not to work, they are guaranteed annual benefits of $$12000.$ Luis also has a choice to work up to $2000$ hours per year, and for every $1$ dollar earn working, they lose $1$ dollar in government benefits.

Based on this information, fill in the columns below.

$\backslash$table$[[$Hours Worked,Government Benefit,Annual Wage,Toal Compensation$],[0,,8,8],[400,0,,],[800,8,,],[1200,0,0.,$a$.],[1600,$or$,0,0],[2000,0,20,0]]$

Given this information, does Luis have an incentive to work?

Yes

No

$1$

$2$

$3$

$6$

$11$

$16$

$7$

$8$

$9$

$12$

$13$

$14$

PROGRESS

Completion

$76\%$