Results 1 to 4 of 4

Math Help - Inequalities help...

  1. #1
    Member
    Joined
    Nov 2007
    Posts
    100

    Inequalities help...

    This question has to be solved using inequalities with the means of a graph. But despite breaking my head on it several times, I am unable to reach a viable solution.

    "A supermarket sells two kinds of washing powder, Sure-clean and Quick-Wash. At least three times as much Sure-Clean is sold as Quick-wash. The supermarket has, at most, 1800cm^2 of shelf space for washing powders. A box of Sure-Clean requires 25cm^2 of shelf space, whilst a box of Quick-wash requires 15cm^2. The profit per box is 8p for Sure-Clean and 12p for Quick-Wash. How many boxes of each kind of powder should be stocked for maximum profit? What is the maximum profit?"

    Please help me setup the inequality. I can handle the graphing and finding the solution for the inequality.

    Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,710
    Thanks
    630
    Hello, struck!

    A supermarket sells two kinds of washing powder, Sure-Clean and Quick-Wash.
    At least three times as much Sure-Clean is sold as Quick-Wash.
    The supermarket has, at most, 1800cm² of shelf space for washing powders.
    A box of Sure-Clean needs 25cm² of shelf space; a box of Quick-wash needs 15cm².
    The profit per box is 8p for Sure-Clean and 12p for Quick-Wash.
    How many boxes of each kind of powder should be stocked for maximum profit?
    What is the maximum profit?
    We have: . \begin{array}{c|c}<br />
& \text{space}  \\ \hline \text{Sure (x)} & 25  \\ \text{Quick (y)} & 15 \\ \hline <br />
\text{Total} & 1800 \end{array}\quad\Rightarrow\quad 25x + 15y \:\leq \:1800

    We are also told that: . x \:\geq \:3y\quad \Rightarrow\quad x -3y \:\geq \:0

    And we have: . P \;=\;8x+12y


    . . Go for it!

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2007
    Posts
    100
    Thanks a lot for that.. but I am not able to graph it ...

    More help please..
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,710
    Thanks
    630
    Hello, struck!


    We assume: . \begin{array}{cccc}x & \geq & 0 & {\color{blue}[1]} \\ y & \geq & 0 & {\color{blue}[2]} \end{array}

    We have: . \begin{array}{cccccccc}25x + 15y & \leq & 1800 & \;\Rightarrow\; & 5x + 3y & \leq & 360 & {\color{blue}[3]}\\<br />
x - 3y & \geq & 0 & \Rightarrow & y & \leq & \frac{1}{3}x & {\color{blue}[4]}\end{array}


    [1] and [2] places us in Quadrant 1.

    Graph the line of [3]: . 5x + 3y \:=\:360
    It has intercepts (72,0) and (0,120).
    Graph the line and shade the region below it.

    Graph the line of [4]: . y \:=\:\frac{1}{3}x
    It contains the origin and has slope 1/3.
    Graph the line and shade the region below it.

    Your graph should look like this:
    Code:
            |
     (0,120)*
            | *
            |   *
            |     *
            |       *           *
            |         *     *
            |           o
            |       *:::::*
            |   *:::::::::::*
          - o - - - - - - - - o - -
            |              (72,0)

    Can you finish it now?

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. inequalities
    Posted in the Algebra Forum
    Replies: 7
    Last Post: August 20th 2011, 04:56 AM
  2. inequalities
    Posted in the Algebra Forum
    Replies: 0
    Last Post: March 20th 2011, 02:42 AM
  3. Inequalities
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 1st 2009, 04:35 AM
  4. Inequalities
    Posted in the Algebra Forum
    Replies: 4
    Last Post: June 15th 2009, 11:26 AM
  5. inequalities
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 14th 2008, 09:57 PM

Search Tags


/mathhelpforum @mathhelpforum