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Math Help - Linear programming problem.

  1. #1
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    Linear programming problem.

    I need some verification on my answer

    A baker wants to make a minimum of 80 gourmet cupcakes and decides to make chocolate and vanilla cupcakes. However to make chocolate cupcakes she needs 2oz of cocoa powder which cost 1$ an oz and can only spend 80$ on powder. She also has a vanilla cupcake oven that can hold a maximum of 90 cupcakes. She can sell chocolate cupcakes for 8$ and vanilla for 6$ how many should she make to maximize revenue.

    I got the constraints X+Y => 80 , 2x,<=80 , and y<=90
    with a final maximum of (40,90) 860$

    Can anyone else do it to see if i got it right?
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  2. #2
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    Re: Linear programming problem.

    Quote Originally Posted by drossi45 View Post
    I need some verification on my answer

    A baker wants to make a minimum of 80 gourmet cupcakes and decides to make chocolate and vanilla cupcakes. However to make chocolate cupcakes she needs 2oz of cocoa powder which cost 1$ an oz and can only spend 80$ on powder. She also has a vanilla cupcake oven that can hold a maximum of 90 cupcakes. She can sell chocolate cupcakes for 8$ and vanilla for 6$ how many should she make to maximize revenue.

    I got the constraints X+Y => 80 , 2x,<=80 , and y<=90
    with a final maximum of (40,90) 860$

    Can anyone else do it to see if i got it right?
    A better idea is for you to show your working, and we'll check it for you.
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  3. #3
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    Re: Linear programming problem.

    Hello, drossi45!

    A baker wants to make a minimum of 80 chocolate and vanilla cupcakes.
    To make chocolate cupcakes. she needs 2 oz of cocoa powder
    which cost $1 an oz and can only spend $80 on powder.
    She also has a vanilla cupcake oven that can hold a maximum of 90 cupcakes.
    She can sell chocolate cupcakes for $8 and vanilla for $6.
    How many should she make to maximize revenue.

    I got the constraints: x+y\,\ge\,80,\;2x\,\le\,80,\;y\,\le\,90
    . . with a final maximum of: (40,90), $860.

    Can anyone else do it to see if i got it right?

    You have the right answer.
    But did you sketch the region correctly?

    Code:
          |
       90 o - - ♥
          |:::::|
       80 o:::::|
          | *:::|
          |   *:|
          |     o
          |     | *
          |     |   *
      - - + - - + - - * - -
          |    40    80
          |
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