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

    Thats what I think, lol, I fail at math!!!
  4. Lakak

    Lakak New Member

    ^Wow, so informative.

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