Going through some old MBA notes, this subject was interesting and I noticed many managers these days ask what is the right mix of workers they need.
Here was a word problem from class that was on this topic.
Production Theory
Miller Corporation's production function is (^2 = squared)
Q = 32E + 20T - 2E^2 - T ^2
The monthly wage of an engineer (E) is $6,000 and the monthly wage of a technician(T) is $3,000. The firm can hire as many as it wants at these wages. If the Miller Corporation decides to spend a total (M) of $51,000 on engineers and technicians, how many engineers and technicians should it hire?
Brings back memories of of math doesn't it?
Here are some calculation notes:
Q = Output
PE = $6,000
PT = $3,000
M = $51,000
1) MPE = 2Q/2E
32-4E
MPT = 2Q/2T
20-2T
2) MPE/PE = MPT/PT
32-4E/6000
20-2T/3000
32-4E = 40-4T
4E-4T-8
E=T-2
3) E x PE + T x PT = M
6,000E+ 3,000T = 51,000
2E+T = 17
4) 2(T-2) + T = 17
T = 7
5)2E + T = 17
E = 5
Check
T x 3,000 + E x 6,000 = 51,000
21,000 + 30,000 = 51,000
Output calc
Q = 32E + 20T - 2E^2 - T ^2
Q = 32(5) + 20(7) - 2 (5^2) - 7^2
Q = 160 + 140 - 50-49
Q= 201
Thank you for following along, this was just to show you it's possible to create functions for your business to help with decision making.