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30 April, 13:10

Irrigation improves the yield of strawberries per acre according to the function S = - (w-2) ^2 + 50 where S is the number of pints of strawberries grown per acre and w is the acre-feet of water used. Strawberries sell for $3 per pint and water costs $5 per acre-foot. Graph the yield function.

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  1. 30 April, 16:21
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    Given:

    The yield of strawberries per acre is

    S = - (w - 2) ² + 50

    where

    S = number of pints of strawberries per acre

    w = acre-feet of water

    Strawberries sell for $3 per pint

    Water costs $5 per acre-feet.

    The yield function is the revenue minus the expenses. It is

    Y = (S pints) * ($3 per pint) - (w acre-ft) * ($5 per acre-ft)

    Y = - 3 (w - 2) ² - 5w + 150 dollars

    A graph of the yield function is shown below.

    It indicates that

    a) the yield is maximum when the acre-feet is about 1.5;

    b) the yield increases between zero and 1.5 acre-feet;

    c) the yield decreases quickly when the acre-feet exceed 1.5;

    d) the yield vanishes when the acre-feet exceed 8.
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