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 $250$ 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 states 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.

a$)$

Determine a minimum$-$cost staffing plan for PharmaPlus. How many pharmacists and technicians are needed?

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$)?$ What will be the impact on the payroll?