Market research predicts that the chain will need to have at least 270 employees total to meet demand in the coming year, so PharmaPlus is advertising to hire new technicians and pharmacists. Each pharmacist earns $50,000 per year and each technician earns $25,000 per year.
Your task is to formulate a linear programming problem to help PharmaPlus determine how many technicians and how many pharmacists to hire. PharmaPlus' objective is to minimize costs while still meeting demand and satisfying the requirements of their quality care guarantee.
You have been asked to use the following variables in your formulation:
P = total number of pharmacists employed
T = total number of technicians employed
a) (10 points) What is the objective function for this linear programming problem?
b) (10 points) Are you trying to maximize or minimize the value of this function? Explain your answer.
c) (30 points) What are the constraints in this linear programming problem? Write the inequalities that describe these constraints below.
|Subject to:||.5 S||+||.4 F||≤||20||(Material 1)|
|.2 S|| || ||≤||5||(Material 2)|
|.3 S||+||.6 F||≤||21||(Material 3)|
a) (30 points) What is the optimal solution to this problem? Circle the point corresponding to this solution on the graph above.
b) (20 points) What materials represent the binding constraints for this problem?