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23 October, 07:33

3. A seafood restaurant owner orders at least 50 fish. He cannot use more than 30 amberjack or more than 35 flounder. Amberjack costs $4 each and flounder costs $3 each. How many of each fish should he use the minimize his cost?

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  1. 23 October, 07:37
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    Refer to the figure shown below.

    Let x = the number of amberjacks

    Let y = the number of flounder

    Because amberjack costs $4 each and flounder costs $3 each, the cost function is

    C = 4x + 3y

    The number of fish is at least 50, therefore

    x + y ≥ 50

    There should be no more than 30 amberjacks and or no more than 35 flounder, therefore

    x ≤ 30

    y ≤ 35

    The solution region for the inequalities is shown shaded. Optimum values of the cost function occur at the vertices.

    The minimum cost occurs at (15,35) and it is C = 4*15 + 3*35 = $165.

    Answer:

    15 amberjack

    35 flounder

    minimum cost = $165
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