Solve using linear programming:

H.P hospital wants to hire nurses and nurse's aides to meet patient needs at minimum cost. The average salary is $65,000 for a nurse and $20,000 for a nurse's aide. The hospital can hire up to 50 people, but needs to hire at least 20 to function properly. The head nurse wants at least 12 aides, but the number of nurses must be at least twice the number of aides to meet state regulations. How many nurses and nurse's aides should be hired to minimize salary costs?

Question

Solve using linear programming:

H.P hospital wants to hire nurses and nurse's aides to meet patient needs at minimum cost. The average salary is $65,000 for a nurse and $20,000 for a nurse's aide. The hospital can hire up to 50 people, but needs to hire at least 20 to function properly. The head nurse wants at least 12 aides, but the number of nurses must be at least twice the number of aides to meet state regulations. How many nurses and nurse's aides should be hired to minimize salary costs?

valpey · Answer

N = # of nurses
A = # of aides
N+A >= 20
N+A <= 50
Cost = $65,000N + $20,000A
A >= 12
N>= 2A

Start with A = 12 and N = 24 and go from there.

anonymous · Answer

ok so is this problem based on logic or common sense?

valpey · Answer

Need to use logic. Common sense can point you toward what seems like most efficient (namely fewer people mean lower costs).

anonymous · Answer

ok so on the last inequality (n>=2a) are the coordinates for the the line (24,0) & (0,12)?

valpey · Answer

This question actually could have been a lot more interesting except that the author has some kind of subconscious axe to grind with state regulations. If you need a map, you are trying to minimize cost over the grid:|dw:1345593093907:dw|