Results 1 to 2 of 2

Math Help - production

  1. #1
    Newbie
    Joined
    Aug 2007
    Posts
    5

    production

    The cost function for producing
    q items is given by
    C(q)=500+15q-250e^-0.04q
    (a) Find the marginal cost when
    q = 0 and when q = 100 and interpret your results.
    (b) Determine the number of items produced so that the marginal cost is less than $20

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    (a) Find the marginal cost when q = 0 and when q = 100 and interpret your results.
    Marginal cost is the first derivative of the cost function.

    C(q) = 500 +15q -250e^(-0.04q)

    d/dx a^u = ln(a) *a^u *du/dx

    So,
    C'(q) = 15 -250[ln(e) *e^(-0.04q) *(-0.04)]
    C'(q) = 15 +(250)(0.04)e^(-0.04q)
    C'(q) = 15 +10e^(-0.04q) ------------------------(i)

    Hence,
    C'(0) = 15 +10e^0 = 15 +10 = 25
    C'(100) = 15 +10e^(-0.04*100) = 15 +0.183 = 15.183

    The marginal cost is decreases as q increases. Marginal cost is inversely proportional to the demand q. ----------------answer.

    (b) Determine the number of items produced so that the marginal cost is less than $20

    C'(q) = 15 +10e^(-0.04q) ------------------------(i)
    15 +10e^(-0.04q) < 20
    10e^(-0.04q) < 5
    e^(-0.04q) < 0.5
    Take the natural logs of both sides,
    (-0.04q)ln(e) < ln(0.5)
    -0.04q < -0.693147
    q < (-0.693147) /(-0.04)

    Division by negative, so reverse the sense of the inequality,

    q > 17.328

    Therefore, so that the marginal cost is less than $20, produce 18 or more items. ---------------answer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Production Costs
    Posted in the Business Math Forum
    Replies: 0
    Last Post: October 16th 2010, 08:02 AM
  2. Optimal production?
    Posted in the Business Math Forum
    Replies: 1
    Last Post: October 1st 2010, 09:28 PM
  3. Rate of oil production..
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 30th 2008, 10:23 PM
  4. production function
    Posted in the Business Math Forum
    Replies: 1
    Last Post: August 19th 2007, 01:21 PM
  5. Production line problem
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: September 4th 2006, 11:37 AM

Search Tags


/mathhelpforum @mathhelpforum