Scenario Question $2(10$ Points$)$: Mexico City Bank of Commerce and Industry is a busy

bank that has requirements for between $10$ and $18$ tellers depending on the time of day.

Lunctime, from noon to $2$:$00$P $>$ M$.,$ is usually heaviest. The following table indicate the

workers needed at various hours that the bank is open.

The bank now employs $12$ full$-$time tellers, but many people are on its roster of available

part$-$time employees. A part$-$time employee must put in exactly $4$ hour per day but can start

anytime between $9$ A$.$M$.$ and $1$ P$.$M$.$ Part$-$timers are a fairly inexpensive labor pool because

no retirement or luch benefits are provided them. Full$-$timers, on the other hand, work from $9$

A$.$M$.$ to $5$ P$.$M$.,$ but are allowed $1$ hour for lunch. $($Half the full$-$timers eat at $11$ A$.$M$.,$ the other

half at noon.$)$ Full$-$timers thus provided $35$ hours per week of productive labor time.

By corporate policy, the bank limits part$-$time hours to a maximum of $50\%$ of the day's total

requirement. Part$-$timers earn $$6$ per hour $($or $$24$ per day$)$ on average, whereas full$-$timers

earn $$75$ per day in salary and benefits on average.

The bank would like to set a schedule, using LP$,$ that would minimize its total manpower

costs. It will release $1$ or more of its full$-$time tellers if it is profitable to do so$.$

We can let:

F$=$ full$-$time tells

P$1=$part$-$timers starting at $9$ A$.$M$.($leaving at $1$ P$.$M$.)$

P$2=$part$-$timers starting at $10$ A$.$M$.($leaving at $2$ P$.$M$.)$

P$3=$part$-$timers starting at $11$ A$.$M$.($leaving at $3$ P$.$M$.)$

P$4=$part$-$timers starting at noon $($leaving at $4$ P$.$M$.)$

P$5=$part$-$timers starting at $1$ P$.$M$.($leaving at $5$ P$.$M$.)$

Part a $(2$ points$).$ Write down the Objective Function

Part b $(2$ points$).$ Write down the constraint for the time period $9$ A$.$M$.$ to $10$ A$.$M$.$

Part c $(2$ points$).$ Write down the constraint for Part$-$time worker$-$hours cannot exceed $50\%$ of

total hours required each day $($which is the sum of the tellers need each hour$)$

Part d $(2$ points$).$ Based on the Excel Solver Answer Report below. How many Full$-$time

workers are hired? And what is the optimal cost?

Part e $(2$ points$).$ The Shadow Price for the R$.$H$.$ Side Constraint of $11$ A$.$M$.$ to noon is $50,$

which allowable increase of $0$ and allowable decrease of $3.$ How to interpret it$.$