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Math Help - Linear Programming - Inequalities help

  1. #1
    Newbie pozmans's Avatar
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    Linear Programming - Inequalities help

    You have a sweet tooth and have a craving for Silky bars and Munchie crunch. You have $20 in your pocket, Silky Bars - $2 and Muinchie Crunch - $2.50. When you get to the shop you find that there are only 5 Silky Bars left.

    How do you write down the contraints as a system of inequalities?
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    Hello, pozmans!

    You have a sweet tooth and have a craving for Silky Bars and Munchie Crunch.
    You have $20 in your pocket.
    Silky Bars cost $2 each and Munchie Crunch cost $2.50 each .
    When you get to the shop you find that there are only 5 Silky Bars left.

    Write the contraints as a system of inequalities.

    Let S = number of Silky Bars: . {\color{blue}S \,\geq\,0}
    Let M = number of Munchie Crunches: . {\color{blue}M \,\geq\,0}

    S Silky Bars at $2 each: 2S dollars (cost)
    M Munchie Crunches at $2.50 each: 2.5M dollars (cost)
    The total cost is: . 2S + 2.5S, which is at most $20.00.
    . . We have: . {\color{blue}2M + 2.5S \:\leq \:20}

    There are only 5 Silky Bars left: . {\color{blue}S \:\leq\:5}


    There are the inequalties: . \begin{Bmatrix}0\:\leq\:S \:\leq \:5 \\ \\[-3mm] M \:\geq\:0 \\ \\[-3mm] 2S + 2.5M \: \leq \: 20 \end{Bmatrix}

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