# Production Theory

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.