Results 1 to 2 of 2

Math Help - Linear Programming-Need help with one problem

  1. #1
    Junior Member
    Joined
    Oct 2007
    Posts
    44

    Exclamation Linear Programming-Need help with one problem

    Can you please help me with the following question?

    An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.

    Objective Function z = 19x + 4y
    Constraints 0 < or equal to x < or equal to 10
    0 < or equal to y < or equal to 5
    3x + 2y > or equal to 6
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by soly_sol View Post
    Can you please help me with the following question?

    An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.

    Objective Function z = 19x + 4y
    Constraints 0 < or equal to x < or equal to 10
    0 < or equal to y < or equal to 5
    3x + 2y > or equal to 6
    Hello,

    the objective function has a straight line as it's graph and the value for z correspond with the y-intercept of this line:

    z = 19x + 4y~\implies~y=-\frac{19}{4}x+\underbrace{\frac z4}_{\text{y-intercept}} . That means: Take the y-intercept from the drawing and multiply it by 4 to get z.

    Constraints:
    \left \{ \begin{array}{l}x\geq 0 \wedge x \leq 10 \\ y\geq0 \wedge y\leq 5 \\y \geq -\frac32 x + 3\end{array} \right. These inequaltities will give a pentagon.

    Now draw parallel lines through the vertices of the pentagon which have the slope m = -\frac{19}{4}. The greater the y-intercept the greater the value for z. If you use the point (10, 5) then the function with the greatest y-intercept is:

    y=-\frac{19}{4}x+\frac {210}{4} . Because \frac14 z = \frac {210}{4} ~\implies~z=210

    Remark:
    (1) I forgot to draw the line: y = -\frac{19}{4} x +5
    (2) the axes have different scales!
    Attached Thumbnails Attached Thumbnails Linear Programming-Need help with one problem-linopt_solysol.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Programming problem
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 29th 2011, 03:45 PM
  2. linear programming problem
    Posted in the Business Math Forum
    Replies: 2
    Last Post: March 9th 2010, 01:10 PM
  3. Linear programming problem
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 8th 2009, 04:32 AM
  4. Linear Programming Problem
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: December 6th 2009, 04:15 PM
  5. Linear Programming Problem
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: July 13th 2008, 08:40 PM

Search Tags


/mathhelpforum @mathhelpforum