1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Minimization problem: Economics: quantity to order

  1. Sep 16, 2018 at 2:34 PM #1
    1. The problem statement, all variables and given/known data
    2. Relevant equations
    Minimum/Maximum occurs when the first derivative=0

    3. The attempt at a solution
    ##Q'=0~## gives no sense result
  2. jcsd
  3. Sep 16, 2018 at 3:50 PM #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You cannot just write ##Q = \sqrt{2(K+pQ)/h}##. You must start the whole modelling procedure over again.

    In the old model, the average cost per week was given as
    $$C(Q) = \frac{KM}{Q} + \frac{1}{2} h Q \; \hspace{2cm} (1) $$
    Solving ##C'(Q)=0## gave the economic order quantity as ##Q = \sqrt{2KM/h}.##

    What is the equation that replaces (1) in the new model?
    Last edited: Sep 16, 2018 at 4:20 PM
  4. Sep 18, 2018 at 11:58 PM #3
    In the old model:
    Where c is the purchase cost of one item. in the new model:
    And differentiating gives the same result
  5. Sep 19, 2018 at 8:12 AM #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper


    BTW: why do you call this thread a "min max" problem? It is a "minimization" problem, but there is no "max" involved. In mathematics, operations research, economics and other such fields the term "min-max" has a definite meaning, and it is nothing like how you use it.
    Last edited: Sep 19, 2018 at 8:37 AM
  6. Sep 19, 2018 at 11:05 AM #5
    Thank you Ray, you are correct, this is only a minimum problem.
    I just automatically wrote the heading.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted