for technicians is $\backslash (\backslash$$ $11\backslash )$ per hour.

$($a$)$ 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 $252\backslash )$

Service quality guideline

$\backslash [$

P$-2$ T $\backslash$geq $0$

$\backslash ]$

Pharmacists employed

$\backslash [$

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

$\backslash ]$

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

$\backslash$$

$\backslash [$

$\backslash$text $\{$ at $\}($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$$ $|$ per hour. The payroll cost using the optimal solution in part $($a$)$ is $\backslash$$ per hour. Thus, the payroll cost will go $---$Select$--$by $\backslash (\backslash$$ $\backslash )$