Century bank has many Spanish speaking customers as well as English speaking customers. To

improve customer experience, the company wants to hire employees with skills in each languge to

be able to antwer all the calla. The consultant company does some further research and finds out

that $20$ percent of the calls are in Spanith and the rest are in Englith.

The consultants observe that an operator can process an average of five calls per hour. The bank has

both full$-$time and part$-$time emplojees avallable to staff the phone lines. A full$-$time employee

works eight hours per day but needs to work on paperwork for four hours each day, so they can

only answer calls for $4$ hours each day. To balance the schedule, the employee alternates shift

petween answering phones and completing paperwork. Full$-$time emplojees can start their day either

by answering phones or by completing paperwork on the first shift. Full$-$time employees speak

either Spanith or English, bat none of them are balingual. Both Spanish$-1$peaking and English$-$

speaking employees are paid $$15$ per hour for work before $5PM$ and $$18$ per hour for work after

$5$ PM$.$ Full$-$time employees can begin work at $7$ AM$,$ or $9$ AM$,$ or $11$ AM$,$ or $1$ PM$.$ Part$-$time

employees work for four bours, only answer calls, and oaly speak English. They can start work at

$3$ PM or $5$ PM$,$ and, like the full$-$time employees, they are paid $$15$ per bour for work before

$5$ PM and $$18$ per hour for work after $5$ PM$.$

For the following analysis, consider only the labor cost for the time employees spend answering

phones. The cost for paperwork time is charged to other cost centers.

Deliverables:

Deliverables are one Excel file that includes the sheets that you work on and a Word file that

includes explanations. The specific deliverables for each step are listed in the relevant step

description. Deliverables should be uploaded by one group member but should include the names of

all group members. Please also indicate each group member's percentage of contribution to the

astignment.

a$.$ Fomulate a lineax programming model to detemine how many full$-$time employees who speak

Spanith, full$-$time employees who ipeak English, and part$-$time employees to start woth in each

shift the bank should hire to minimize operating costs while answering all calls. Write the

algebraic formulation of the linear programming problem in the Word file.

b$.$ Obtain an optimal solution for the linear programming model formulated in part $k$ using Excel

Solver $($Show your work in Excel and please write an explanation in the Word file$).$

c$.$ Because many full$-$time workers do not want to work late into the evening, the bank can find

only cae qualified English$-$speaking operator willing to begin work at $1$ PM$.$ Giren this new

d$.$ The bank now has decided to investigate the option of hiring bilingual

operators instead of monolingual operators. If al$1$ employees are bilingual,

how many fu$11-$time and part$-$time employees should the bank hire to begin on

each shift to minimize operating costs while answering all calls? As in

part a$,$ formulate a linear programing mode$1$ to guide the bank' $s$ decision.

$($Show your work in Excel and please write an explanation in the Word file$)$

e$.$ Obtain an optimal solution for the linear programming model formulated in

part $d$ using Exce$1$ Solver. $($Show your work in Exce$1$ and please write an

explanation in the Word file$)$