Question

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.

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

1. Let P	=	number of full-time equivalent pharmacists
   T	=	number of full-time equivalent technicians

Min or Max ___P+____T

____P+____T _____ (less than or equal to, greater than or equal to, equal) ____ Full-time -equivalent employees_

____P- ____T _____ (less than or equal to, greater than or equal to, equal) ____ Quality Guideline

____P ____ (less than or equal to, greater than or equal to, equal) ____ Number of pharmacists

The optimal solution requires ____ full-time equivalent pharmacists and ____ full-time equivalent technicians. The total cost is $ ____ per hour.

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)?

	New Hires Required
Pharmacists
Technicians

What will be the impact on the payroll?

The payroll cost will ____ by $ ____ per hour.

Answer 1

Let P	=	number of full-time equivalent pharmacists
T	=	number of full-time equivalent technicians

MinZ = $35P + $15T

S.T. 100 P + 175T >= 280 Full-time-equivalent employees

P - 2T >= 30 Quality guidlines

10 P >= 15 No. of pharmacists

and P, T >= 0

Solving by Simplex method using P = x1 and T = x2

Similarly we do next steps

Hence the new hired required =P = 30, T = 0

Optimal solution Min Z = 35 P + 15T

35 (30) + 15 (0) = 1050