need math help.. max/min problems

[BlazeUp]

I'm not very good with these at all..

1. Suppose that the demand function for a monopolist's product is of the form q=Ae^-Bp for positive constants A and B. In terms of A and B, find the value of p for which maximum revenue is obtained. Can you explain why your answer does not depend on A?

This one i have no idea how to start. Im guessing it doesnt depend on A because its a constant and it doesnt change when derivative is taken

2. For a monopolist, the cost per unit of producing a product is $3, and the demand equation is p=10/sqrt(q). What price will give the greatest profit?

i have: P=r-c
P(q)=10q/sqrt(q) - 3q but it doesnt work out properly so i need help

3. For a monopolist's product, the demand function is p=40/sqrt(q) and the average-cost function is c=1/3+2000/q. Find the profit maximizing price and outpute. At this level, showt hat marginal revenue is equal to marginal cost.



4. For a manufacturer, the cost of making a part is $30 per unit for labor and $10 per unit for materials; overhead is fixed at $20000 per week. If more than 5000 units are made each week, labor is $45 per unit for those units in excess of 5000. At what level of production will average cost per unit be a minumum?

my guess is c=40x+20000 then idk what to do with the second part of this question

 

[NoPoke]

okay I'm going to guess at what the letters mean.

q = quantity produced (demand?)
p = price

so revenue = qp

1) revenue = Ap e^(-Bp)

differentiate and set to zero to find minima/maxima

2) profit = q(p - $3)

you want a relationship between profit and price so eliminate q.

q = 100/(p^2)

substitute then differentiate and set to zero to find maxima/minima

3) I don't know what marginal revenue and marginal cost are so can't help with the math

4) draw a graph. First draw the line representing cost per unit up to 5000 units, then draw the line representing the cost per unit when production exceeds 5000 units.


==============

Hope that helps and fingers crossed I've not made a simple error.

 

[Vegeta ss4]

ummm.....E=mc²
Thats what I think, lol, I fail at math!!!

 

[Lakak]

^Wow, so informative.