per hour.

Determine a minimum$-$cost staffing plan for PharmaPlus. $($Let $\backslash ($ P $\backslash )$ be the number of full$-$time equivalent pharmacists. Let $\backslash ($ T $\backslash )$ be the number of full$-$time equivalent technicians.$)$

Min

s$.$t$.$

Employees $($pharmacists and technicians$)$ required $\backslash (\backslash$quad P$+$T $\backslash$geq $264\backslash )$

Service quality guideline

Pharmacists employed

$\backslash ($ P$,$ T $\backslash$geq $0\backslash )$

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

$\backslash$$ $7332$ at $\backslash (($P$,$ T$)=(\backslash$quad$)\backslash )$

$($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 $\backslash (\backslash$$ $6695\backslash )$

per hour. The payroll cost using the optimal solution in part $($a$)$ is $\backslash (\backslash$$ $7332\backslash )7332$

per hour. Thus, the payroll cost will go by $\backslash$$ $37.$