math

1. A farmer has 100 acres of land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hours of labor and $20 of capital, and each acre of corn requires 16 hours of labor and $40 of capital. The farmer has at most 800 hours of labor and $2400 of capital available. If the profit from an acre of wheat is $80 and from an acre of corn is $100, how many acres of each crop should she plant to maximize her profit?

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  1. c = acres of corn
    w = acres of wheat

    constraints:

    c+w </= 100
    graph that line,shade under

    wheat cost = 20 w
    corn cost = 40 c
    20 w + 40 c </= 2400
    graph that line, shade under

    wheat labor = 4 w
    corn labor = 16 c
    4 w + 16 c </= 800
    graph that line, shade under

    Now the criterion
    p = 80 w + 100 c

    check p at every intersection of the above constraint lines, pick the biggest p

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  2. Let X be the area for wheat (in acres), and
    Let Y be the area for corn.

    The amount of labor is 5X + 15Y hours.
    The amount of capital is 20X + 30Y dollars

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  3. Corn: 0 , Wheat: 120

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  4. Yes am learning

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