Math

Suppose that y≤3⁢x, 2⁢x≤y and 13⁢x+13⁢y≤1 together with 0≤x, 0≤y.
Determine a value of k so that the function f(x,y)=kx=y has a positive maximum value on the region at two corners.

ANS: k= ?

  1. 👍 0
  2. 👎 0
  3. 👁 303
  1. We cannot read the question because of unknown encoding.
    Please specify character encoding used (language) or post the character before x and y in the constraints.
    If it is √() you can write sqrt() instead.

    Also, check if the last equation has been posted correctly.
    Is it
    f(x,y)=kx=y
    or
    f(x,y)=kx-y
    ?
    Thank you.

    1. 👍 0
    2. 👎 0
  2. Suppose that y≤3x, 2x≤y and 1/3x+1/3y≤1 together with 0≤x, 0≤y.
    Determine a value of k so that the function f(x,y)=kx+y has a positive maximum value on the region at two corners.

    ANS: k= ?

    1. 👍 0
    2. 👎 0
  3. Use your calculator to plot three graphs, as follows:
    http://img203.imageshack.us/i/1299091442.png/
    This way, you have an idea what to look for.

    The lines are:
    (blue) f1(x)=y=3x
    (red) f2(x)=y=2x
    (green) f3(x)=y=x/(3x-1)

    The region that satisfies all the constraints are between the red and blue lines, and below the green curve.

    To find the value of k you need to find the coordinates of the two intersection points of the (green) curve with the straight lines.

    This you can obtain by solving the following equations:
    f1(x)=f3(x) => 3x=x/(3x-1)....(1)
    f2(x)=f3(x) => 2x=x/(3x-1)....(2)

    These are quadratics and provide two roots each:
    Solution to (1): (x=0 or) x=4/9, y=4/3
    Solution to (2): (x=0 or) x=1/2, y=1

    Therefore f(x,y)=kx+y must pass through (4/9,4/3) and (1/2,1) to satisfy the last requirement. The value of k is the slope of the line passing through these two points using the usual formula:
    Slope, k = (y2-y1)/(x2-x1)

    Can you take it from here?

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra worksheet

    Hello. My algebra teacher gave me this worksheet last week and everyone had to bring it yesterday and I haven't done it yet. Can someone please help me. He said Friday is the last day or he's going to take away some points. I've

  2. Physics

    Running on a treadmill is slightly easier than running outside because there is no drag force to work against. Suppose a 60 kg runner completes a 5.0 km race in 19 minutes. Part A Determine the drag force on the runner during the

  3. Math

    Suppose $p(x)$ is a monic cubic polynomial with real coefficients such that $p(3-2i)=0$ and $p(0)=-52$. Determine $p(x)$ (in expanded form).

  4. Physics

    The ski slopes at Bluebird Mountain make use of tow ropes to transport snowboarders and skiers to the summit of the hill. One of the tow ropes is powered by a 22-kW motor which pulls skiers along an icy incline of 14° at a

  1. Physics

    suppose that two point charges each with a charge of +1 coulomb are separated by a distance of 1 meter will they attract or repel ? determine the magnitude of the electrical force between them

  2. physics

    C Exercise 3.57 In laboratory situations, a projectile’s range can be used to determine its speed. To see how this is done, suppose a ball rolls off a horizontal table and lands 1m out from the edge of the table. Part A If the

  3. Physics-calc

    Suppose the position of an object is given by ->r(vector) = (3.0t^2*ihat - 6.0t^3*jhat)m. Where t in seconds. Determine its velocity ->v as a function of time t. Determine its acceleration ->a as a function of time t. Determine

  4. Math

    Let A , B , and C be events associated with the same probabilistic model (i.e., subsets of a common sample space), and assume that P(C)>0 . For each one of the following statements, decide whether the statement is True (always

  1. Chemistry

    Suppose you are given a sample of a homogeneous liquid. What would you do to determine whether it is a solution or a pure substance?

  2. trig

    Suppose that sin x = 1/5 and cos y = 2/3, and x and y are each angles in Quadrant 1. Determine sin(x+y).

  3. Repost physics

    Suppose the position of an object is given by ->r(vector) = (3.0t^2*ihat - 6.0t^3*jhat)m. Where t in seconds. Determine its velocity ->v as a function of time t. Determine its acceleration ->a as a function of time t. Determine

  4. Probability

    Determine whether each of the following statements about events A,B,C is always true or not. 1. Suppose that A,B and C are independent events; then A^c (A complement) and B U C^c are independent. (T/F) 2. From now on, we do not

You can view more similar questions or ask a new question.