Question $21(30$ points$)$

Answer all questions $(30$ points$).$

Consider the following data for an economy last year:

Total population

$405\mathrm{.}15$ million

Part$-$time workers looking for full$-$time jobs

$6\mathrm{.}58$ million

Unemployed workers who are not actively searching

for jobs

$8\mathrm{.}32$ million

Retirees and stay$-$home parents

$20\mathrm{.}58$ million

Unemployed workers who are actively searching for

jobs

$12\mathrm{.}25$ million

Population under $16$ years old and or institutionalized $56\mathrm{.}05$ million

Unemployed full$-$time college students

$65\mathrm{.}75$ million

$($a$)$ With the data above, determine the economy's official $($i$)$ labor force and $($ii$)$

unemployment rate. Clearly show your steps and calculations, including the

economic factors involved.