Write Sensitivity analysis for the case study below

The King's Landing Amusement Park

King's Landing is a large amusement theme park located

in Virginia. The park hires high school and college stu$-$

dents to work during the summer months of May, June,

July, August, and September. The student employees oper$-$

ate virtually all the highly mechanized, computerized rides;

perform as entertainers; perform most of the custodial work

during park hours; make up the workforce for restaurants,

food services, retail shops, and stores; drive trams; and park

cars. Park management has assessed the park's monthly

needs based on previous summers' attendance at the park

and the expected available workforce. Park attendance is

relatively low in May, until public schools are out, and then

it increases through June, July, and August, and decreases

dramatically in September, when schools reopen after

Labor Day. The park is open $7$ days a week through the

summer, until September, when it cuts back to weekends

only. Management estimates that it will require $22,000$

hours of labor in each of the first $2$ weeks of May, $25,000$

hours during the third week of May, and $30,000$ hours dur$-$

ing the last week in May. During the first $2$ weeks of June,

it will require at least $35,000$ hours of labor and $40,000$

hours during the last $2$ weeks in June. In July $45,000$ hours

will be required each week, and in August $45,000$ hours

will be needed each week. In September the park will need

only $12,000$ hours in the first week, $10,000$ hours in each of

the second and third weeks, and $8,000$ hours the last week

of the month.

The park hires new employees each week from the first

week in May through August. A new employee mostly trains

the first week by observing and helping more experienced

employees; however, he or she works approximately $10$

hours under the supervision of an experienced employee. An

employee is considered experienced after completing $1$ week

on the job. Experienced employees are considered part$-$time

and are scheduled to work $30$ hours per week to eliminate

overtime and reduce the cost of benefits, and to give more

students the opportunity to work. However, no one is ever laid

off or will be scheduled for fewer $($or more$)$ than $30$ hours,

even if more employees are available than needed. Manage$-$

ment believes this is a necessary condition of employment

because many of the student employees move to the area

during the summer just to work in the park and live near the

beach nearby. If these employees were sporadically laid off

and were stuck with lease payments and other expenses, it

would be bad public relations and hurt employment efforts

in future summers. Although no one is laid off, $15\%$ of all

experienced employees quit each week for a variety of rea$-$

sons, including homesickness, illness, and other personal

reasons, plus some are asked to leave because of very poor

job performance.

Park management is able to start the first week in May

with $700$ experienced employees who worked in the park in

previous summers and live in the area. These employees are

generally able to work a lot of hours on the weekends and

then some during the week; however, in May attendance is

much heavier on the weekends, so most of the labor hours

are needed then. The park expects to have a pool of $1,500$

available applicants to hire for the first week in May. After

the first week, the pool is diminished by the number of new

employees hired the previous week, but each week through

June the park gets $200$ new job applicants, which decreases

to $100$ new applicants each week for the rest of the sum$-$

mer. For example, the available applicant pool in the second

week in May would be the previous week's pool, which in

week $1$ is $1,500,$ minus the number of new employees hired

in week $1$ plus $200$ new applicants. At the end of the last

week in August, $75\%$ of all the experienced employees will

quit to go back to school, and the park will not hire any new

employees in September. The park must operate in Septem$-$

ber, using experienced employees who live in the area, but

the weekly attrition rate for these employees in September

drops to $10\%.$

Formulate and solve a linear programming model to

assist the park's management to plan and schedule the

number of new employees it hires each week to minimize

the total number of new employees it must hire during the

summer.