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# Linear Programming : Finding Constraints

PharmaPlus operates a chain of 30 pharmacies. The pharmacies are staffed by licensed pharmacists and pharmacy technicians. The company currently employs 85 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 250 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 stated 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 \$40 per hour and the average salary for technicians is \$10 per hour.
a. Formulate a linear programming model that can be used to determine a minimum-cost staffing plan for PharmaPlus.
b. Determine the optimal staffing plan using the Management Scientist software, including the number of pharmacists and technicians needed.
c. Given current staffing levels and expected attrition, determine the number of new hires (if any) that must be made to reach the level recommended in part (a). Explain the impact (if any) on the payroll.

#### Solution Preview

Let's analyze the conditions of the problem.
Let X1 denote the number of pharmacists to be hired, X2 denote the number of technicians to be hired.

1. Currently the company employs 85 pharmacists and 175 technicians. So there are 85+175=260 employees.
2. At least 250 employees are required in the next year. But the company already has 260 employees. Don't worry. Let's look at the next statement.
3. It is expected that 10 pharmacists and 30 technicians will leave in the ...

#### Solution Summary

LP is used to find constraints. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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