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Thread: Can someone help with this Algebra 1 problem?

  1. #1

    Can someone help with this Algebra 1 problem?

    Paul sells chocolate chip cookies and peanut butter cookies.
    Baking a batch of chocolate chip cookies takes 1.75 cups of flour and 2 eggs.
    Baking a batch of peanut butter cookies takes 1.25 cups of flour and 1 egg.

    Paul has 10 cups of flour and 12 eggs.

    He makes $4 profit per batch of chocolate chip cookies.
    He makes $2 profit per patch of peanut butter cookies.

    How many batches of peanut butter cookies should Paul make to maximize his profits?


  2. #2
    Senior Member
    Join Date
    Sep 2012
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    2,229
    Quote Originally Posted by Evelyn3131 View Post
    Paul sells chocolate chip cookies and peanut butter cookies.
    Baking a batch of chocolate chip cookies takes 1.75 cups of flour and 2 eggs.
    Baking a batch of peanut butter cookies takes 1.25 cups of flour and 1 egg.

    Paul has 10 cups of flour and 12 eggs.

    He makes $4 profit per batch of chocolate chip cookies.
    He makes $2 profit per patch of peanut butter cookies.

    How many batches of peanut butter cookies should Paul make to maximize his profits?

    Evelyn

    It is very hard to help you with this problem because we have no idea what mathematical tools are in your personal tool kit.

    Let's start by asking some questions. What is the highest number of batches of chocolate cookies (my favorites) that Paul can make, given that each batch requires 2 eggs and he has only 12 and each batch requires 1.75 cups of flour and he has only 10 cups? What would his profit be if he made that many batches of chocolate chips?

  3. #3
    Elite Member
    Join Date
    Jan 2005
    Location
    Lexington, MA
    Posts
    5,686
    Hello, Evelyn3131!

    Is there a typo?
    This is not a "good" Linear Programming probem.

    Paul sells chocolate chip (CC) cookies and peanut butter (PB) cookies.

    Baking a batch of CC cookies takes 1.75 cups of flour and 2 eggs.
    Baking a batch of PB cookies take 1.25 cups of flour and 1 egg.
    Paul has 10 cups of flour and 12 eggs.

    He makes $4 profit per bath of CC cookies.
    He makes $2 profit per batch of PB cookies.

    How many batches of PB cookies should Paul make to maximize his profit?

    . . [tex]\begin{array}{c|c|c|} & \text{flour} & \text{eggs} \\ \hline \text{CC (x)} & 1.75 & 2 \\ \text{PB (y)} & 1.25 & 1 \\ \hline \text{Total} & 10 & 12 \\ \hline \end{array}[/tex]

    We have these inequalities: .[tex]\begin{Bmatrix}1.75x + 1.25y \:\le\:10 \\ 2x + y \:\le\:12 \\ x\:\ge\:0 \\ y \:\ge\:0 \end{Bmatrix}[/tex]

    Profit function: .[tex]P \:=\:4x + 2y[/tex]


    When we graph the two lines,
    . . we find that they do not intersect in Quadrant 1.

    The graph looks like this:

    Code:
          |
          |
          *
          | *
          |   *
          |     *
          *       *
          |  *      *
          |     *     *
          |        *    *
        --+-----------*---*----
          |

  4. #4
    Elite Member
    Join Date
    Feb 2004
    Location
    Ottawa, Ontario
    Posts
    16,365
    Code:
    5 CC  :  8.75 cups + 10 eggs
    1 PB  :  1.25 cups +  1 egg
    ============================
    TOTAL : 10.00 cups + 11 eggs
    5 @ $4 + 1 @ $2 = $22

    And you have an egg left for breakfast
    I'm just an imagination of your figment !

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