$1.$ Ken Stark is an operations analyst for an insurance company in Muncie, Indiana. Over the next $6$ weeks the company needs to send $2,028,415$ pieces of marketing literature to customers in the following $16$ states:

State

Mailing pieces

State

Mailing pieces

AZ

$82,380$

MT

$33,309$

CA

$212,954$

NC

$170,997$

CT

$63,796$

NJ

$104,974$

GA

$136,562$

NV

$29,608$

IL

$296479$

OH

$260,858$

MA

$99070$

OR

$63,605$

ME

$38848$

TX

$214,076$

MN

$86207$

VA

$134,692$

In order to coordinate with other marketing efforts, all the mailings for a given state must go out the same week $($i$.$e$.,$ if Ken decides to schedule mailings for Georgia in week $2,$ then all of the $136,562$ pieces of mail for Georgia must be sent that week$).$ Ken would like to balance the work load in each week as much as possible and, in particular, would like to minimize the maximum amount of mail to be processed in any given week during the $6-$week period.

a$.$ Create a spreadsheet model to determine which states should be processed each week in order to achieve Ken$$s objective.

b$.$ What is the optimal solution?