need math help.. max/min problems

Discussion in 'Random Topic Center' started by BlazeUp, Feb 14, 2008.

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  1. BlazeUp

    BlazeUp New Member

    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
     
  2. NoPoke

    NoPoke New Member

    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. :)
     
    Last edited: Feb 15, 2008
  3. Vegeta ss4

    Vegeta ss4 Iron Chef Leader

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

    Lakak New Member

    ^Wow, so informative.
     

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