Math Is Fun Forum

spmishra9

Novice

Registered: 2023-11-22

Posts: 1

A maximization problem

Consider the following function.

P=(A-b(q+r)^m)-c)q

What would be the above function maximizing value of q?

A step-wise detailed guidance would be really helpful. Thanks so much.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: A maximization problem

hi spmishra9

Welcome to the forum.

P=(A-b(q+r)^m)-c)q

Hmm. I've got several questions about this.

Firstly, that formula has 2 open brackets but 3 close brackets. It makes a difference to any calculation.

Next I'm unclear about what you are trying to maximise.

maximizing value of q

Do you mean vary q so that P is maximised?

It also depends on the sign of m and b. eg. if m is negative it changes the way P varies.

Thinking about it some more, I think the sign of every letter affects the outcome.

Please start by clearing up the bracket situation. I'll post back a formula in mathematical appearance so there no ambiguity and hopefully we can move to an answer.

later edit: I made up some numbers and tried getting a graph.  Negative m doesn't seem to have an upper bound for P. When m is positive there's a clear maximum in positive q so I'm guessing that's what you're after. So I would probably differentiate to find the maximum. But I need a bracket consistent formula to do that properly please.

Bob

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Children are not defined by school ...........The Fonz
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Sometimes I deliberately make mistakes, just to test you!  …………….Bob