PharmaPlus operates a chain of $30$ pharmacies. The pharmacies are staffed by licensed pharmacists and pharmacy technicians. The company currently employs $100$ 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 $280$ 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$$s new service quality guidelines specify no more than two technicians per licensed pharmacist. The average salary for licensed pharmacists is $$35$ per hour and the average salary for technicians is $$15$ per hour.

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

Let P $=$ number of full$-$time equivalent pharmacists

T $=$ number of full$-$time equivalent technicians

fill in the blank $2$

P $+$ fill in the blank $3$

T

s$.$t$.$

fill in the blank $4$

P $+$ fill in the blank $5$

T

fill in the blank $7$

Full$-$time$-$equivalent employees

fill in the blank $8$

P $-$ fill in the blank $9$

T

fill in the blank $11$

Quality guideline

fill in the blank $12$

P

fill in the blank $14$

Number of pharmacists

The optimal solution requires fill in the blank $15$

full$-$time equivalent pharmacists and fill in the blank $16$

full$-$time equivalent technicians. The total cost is $fill in the blank $17$

per hour.

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

New Hires Required

Pharmacists fill in the blank $18$

Technicians fill in the blank $19$

What will be the impact on the payroll?

The payroll cost will

by $ fill in the blank $21$

per hour.