Results 1 to 2 of 2

Math Help - Max Profit

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    90

    Max Profit

    This problem makes no sense to me

    A store can sell 20 bikes per week at $400. For each $10 the store lowers the price by 2 more bicycles sold per week. each buke costs the store 200 dollars what price should be charged to maximize profit? how many bikes sold?

    I have no clue how to formulate my cost and revenue functions from this
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Apr 2009
    Posts
    4
    First you need to create the demand function to relate revenue to the price increase\decrease. To do this you will need to find another point to calculate the slope. I picked the point 22, 390 ($10 decrease 2 bikes sold increase).

    Now I calculate the slope (390-400)/(22-20)=-5. Now you can put this into slope intercept form with the original pts. y-400=-5(x-20) sim: y=-5x+300.

    Now we can create the primary function. Profit is Revenue - Cost. What is the revenue in this case? It is number of units sold multiplied by price. This is x*y. Y is related to x via the demand function we just created. What is the cost? The cost is a given, and it is $200. However, we must remember to multiply it by the number of units sold; so for the function the cost is 200x.

    So the primary function will be P(x)=x*(-5x+300)-200x. sim: -5x^2+100x

    Now we can differentiate and solve for zero to find critical values and possible mins and maxes.

    -10x+100=0
    -10x=-100
    x=10

    Maximum profit will be made when 10 units are sold. Given our earlier relationship we know that the cost per unit will be $250. The cost will be $2000, so the max profit that can be made is $500.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Profit
    Posted in the Algebra Forum
    Replies: 3
    Last Post: January 10th 2011, 02:54 AM
  2. Profit >=0
    Posted in the Business Math Forum
    Replies: 0
    Last Post: April 21st 2009, 09:48 AM
  3. profit and marginal profit relationship
    Posted in the Business Math Forum
    Replies: 1
    Last Post: January 16th 2009, 08:00 AM
  4. profit
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: October 13th 2008, 02:49 PM
  5. Profit
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 19th 2007, 12:15 AM

Search Tags


/mathhelpforum @mathhelpforum