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Optimization Problem - Part A

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.

Regards,

math rookie

Re: Optimization Problem - Part A

Hey fagipop.

For your question is the quantity A, a constant?

Re: Optimization Problem - Part A

Hi Chiro,

Many thanks for your help. Yes A is to be a constant.

Re: Optimization Problem - Part A

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?

Re: Optimization Problem - Part A

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?

thx

Re: Optimization Problem - Part A

I just noticed you said A was a constant but you are differentiating with respect to A in your answer. Does this mean A is not a constant?

Re: Optimization Problem - Part A

Sorry - yes you are right. It is not a constant - it has to vary as the number of adverts will constitute to demand variable q.

Re: Optimization Problem - Part A

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.