For your question is the quantity A, a constant?
Hi Fellow Maths Friends,
Going through a problem set and stuck on solving part A of Question 1. Could someone assist and advise if I am on the right track? The figures as I am simplifying seem to be quite large and non elegant. Sorry for the light scan - you may have to highlight page to make darker.
Thanks heaps for your help.
So to start you off, turning points in functions occur when you have a minimum or a maximum and when the second derivative is non-zero (it's not a local minimum or a local maximum: you have to check that later on).
The turning points occur when f'(x) = 0 and a maximum occurs when f''(x) < 0 and a minimum occurs when f''(x) > 0.
Can you calculate these quantities first?
yes - I have attached my initial attempts in the scan doc - its page 2 onwards behind the question page. I have started by introducing equation Profit = PQ - C (Introduced as Price * Quantity - Cost)
Variable A and Q have been solved. Is this correct thus far?
If there are no constraints on your optimization problem, then your approach is good (it doesn't say there are in the question, but it's always a good idea to check).
If you have constraints, then you need to use what is called Lagrange Multipliers to do the optimization.
I didn't check the algebra though, but a good way to check these kind of things is to plot the graph (especially around the neighbourhood) to verify that you have a maximum or a minimum. It doesn't mean it is the global maximum or minimum, but it's a way to re-inforce your algebra.