Problem $7-49($Algorithmic$)$

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.

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

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

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

$\backslash$table$[[$Min$,40,,+,10,,,],[$s$.$t$.],[,$f$,,+,|T|,,,250,$Full$-$time$-$equivalent employee$],[,$F$,,-,=\sqrt[\phantom{2}]{5},,,0,$Quality guideline$],[,1,$p$,,,,,90,$Number of pharmacists$]]$

The antimal colution renuirec on full$-$time enuivalent nharmarists and $1n$ fill$-$time enuivalent terhniriane The tntal rnct is &