how many teachers and TA's the program should hire to minimize costs. what is the minimum cost?

Question

 Northwestern is looking to hire teachers and TA’s to fill its staffing needs for its summer program at minimum cost. The average monthly salary of a teacher is $2400 and the average monthly salary of a TA is $1100. The program can accommodate up to 45 staff members and needs at least 30 to run properly. They must have at least 10 TA’s and may have up to 3 TA’s for every 2 teachers. Using Python, find how many teachers and TA’s the program should hire to minimize costs. What is the minimum cost?  

Answer 1

Some simple math indicates 18 TA's and 12 teachers. To get to the lowest cost you need the maximum allowed TA's in relation to teachers. The max TA's is 3 for every 2 teachers. You also want to minimize the overall staff. The smallest staff that the requirement allow is 30. Both conditions are satisfied by the suggested answer. A program isn't really needed.

 

# Here is what one that solves this problem might look like.

best_cost = None

for ta in range(30): # 0 thru 29 ta's

  te = 30 - ta # calculate number of teachers that adds up to minimum staff

  if ta / te  > 3 / 2:

   break # too many ta, you can stop

  cost = ta * 1100 + te * 2400 # calculate cost

  if best_cost is None or cost < best_cost:

   best_cost = cost

   best_ta = ta

   best_te = te

print( "Best cost:", best_cost, "TA s:", best_ta, "Teachers:", best_te);