PharmaPlus operates a chain of $30$ pharmacies. The pharmacies are staffed by licensed pharmacists and pharmacy technicians. The company currently employs $85$ full$-$time equivalent pharmacists $($combination of full time and part time$)$ and $175$ full$-$time equivalent technicians. Each spring management reviews current staffing levels and makes hiring plans for the year. A recent forecast of the prescription load for the next year shows that at least $263$ full$-$time equivalent employees $($pharmacists and technicians$)$ will be required to staff the pharmacies. The personnel department expects $10$ pharmacists and $30$ technicians to leave over the next year. To accommodate the expected attrition and prepare for future growth, management stated that at least $15$ new pharmacists must be hired. In addition, PharmaPlus's new service quality guidelines specify no more than two technicians per licensed pharmacist. The average salary for licensed pharmacists is $$40$ per hour and the average salary for technicians is $$10$ per hour.technicians is $$10$ per hour.

Min

s$.$t$.$

Employees $($pharmacists and technicians$)$ required

Service quality guideline

Pharmacists employed

$P,T0$

How many pharmacists and technicians are needed? What is the Optimal Objective Value?

$($b$)$ Given current staffing levels and expected attrition, how many new hires $($if any$)$ must be made to reach the level recommended in part $($a$)?$

Additional Pharmacists to hire

Additional Technicians to hire

What will be the impact on the payroll?

The payroll cost using the current levels of $85$ pharmacists and $175$ technicians is $

per hour. The payroll cost using the optimal solution in part $($a$)$ is $

per hour. Thus, the payroll cost will go ${?}_{---\text{S}\text{e}\text{l}\text{e}\text{c}\text{t}--vby}$$