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

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

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


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

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