Math

After experimentation, a certain manufacturer determined that if x units of a particular commodity are produced per week, the marginal cost is given by 0.3x -11, where the production cost is in dollars. If the selling price of the commodity is fixed at $19 per unit, and the fixed cost is $100 per week, find the maximum profit that can be obtained.

  1. 👍 0
  2. 👎 0
  3. 👁 128
asked by Jai
  1. for x units, the profit p(x) is
    p(x) = 19x-100-c(x)
    where c(x) is the cost of the units.
    now,
    dc/dx = .3x-11, so c(x) = 0.15x^2-11x (why no +C?)
    p(x) = 19x-100-(0.15x^2-11x)
    = -0.15x^2 + 30x - 100
    now just find the vertex of that parabola for maximum profit.

    1. 👍 0
    2. 👎 0
    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    A manufacture of a certain commodity has estimated that her profit in thousands of dollars is given by the expression -6x^2+30x-10 where x (in thousands) is the number of units produced. What production range will enable the

    asked by Math on May 26, 2011
  2. Statistics

    A manufacturer estimates that when x units of a particular commodity are produced each month, the total cost (in dollars) will be C(x) = 1/8x^2+4x+200 and all units can be sold at a price of p(x) = 49 - x dollars per unit.

    asked by Jack on March 3, 2017
  3. Economics

    The fixed cost of producing five units of a particular commodity is given as #900 while the total cost of producing the same five units of this commodity is #1000.the marginal cost of the 6th unit produced later is #200.calculate

    asked by Daniel on April 9, 2017
  4. Calculus

    A manufacturer determines that the profit derived from selling x units of a certain item is given by: P = − 2x^2 +800x Find the marginal profit for a production of 20 units. Also, The demand function for a particular commodity

    asked by John on August 23, 2011
  5. economic theory

    assume that a business firm produces two commod ities, X and Y, with two different inpu ts, Labour (L) and Capital (K). The total quantities of L and K available per un it of time are specified as L = 1600 labour hours; and K = 20

    asked by john on February 9, 2015
  1. Math

    a manufacturer has daily production costs of C=4000-30x+0.5x where C is the total cost in dollars and x is the number of units produced. (a) How many units should be produced each day to yield a minimum cost? (b) What is the

    asked by Joe on October 21, 2015
  2. Marketing

    A manufacturer of AC units realizes a cost of $55.00 for every unit produced. Its total fixed cost is $2,000,000. If the manufacturer produces 500,000 units, calculate its: a. unit cost b. markup price if it desires a 10% returns

    asked by Craig on July 12, 2010
  3. Math

    A manufacturer estimates that the profit P from producing x units of a commodity is P=-x^2+40x-100 dollars per week. What is the maximium profit he can realize in one week? I was going to take the derivative of the equation and

    asked by Hannah on February 26, 2011
  4. Economics

    Can you tell me please if my answer is right to the following question? The question: present Adam Smith's theory of value and limitations. 1. Labor cost: he supported that everyone must produce his own goods using own labor and

    asked by Anna on February 25, 2012
  5. Economics

    adam smith supported three different views of theory of value (are the followings correct, i will add them to my essay) 1. Labor cost: he supported that everyone must produce his own goods using own labor and exchange the surplus

    asked by Ana on February 25, 2012

More Similar Questions