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    Graphing and Harvesting Functions

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    x = a1*x - a2*x^2 - h a1 > 0, a2 > 0, h>0

    1. |x| = tons and |x| = tons/years
    What are the dimensions of a1, a2, and h?
    (see attached file for more details)

    2. Use the quadratic formula to show that the phase diagrams (x vs. x)have no intercepts:
    (see attached file for more details)

    3. If h < a1^2/(4a2) , x vs. x will have 2 intercepts, what are the signs ( + or - )?

    4. Plot x* vs. x for h = a1^2/(4*a2) , h < a1^2/(4*a2) , h > a1^2/(4*a2)
    (see attached file for more details)

    5. Normalize and non-dimensionalize the harvesting equation using the variable
    (see attached file for more details)

    6. If h < a1^2/(4*a2), what is the magnitude for h*? What is the equilibrium value for x*?
    7. How do the values in number 6 relate to the h = a1^2/4*a2 phase diagram?

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    The solution discusses graphing and harvesting functions.