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Math Help - The graph to the right shows a region of feasible solutions IMG included

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    The graph to the right shows a region of feasible solutions IMG included

    The graph to the right shows a region of feasible solutions. Use this region to find the maximum and minimum values of the given objective functions, and the locations of these values on the graph.

    A. z = 0.60x + 0.50y
    B. z = 2.25x + 1.25y

    Here is a photo of the graph:

    Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting


    A. The max value of the objective function z = 060x + 0.50y is?

    The value is located at?

    The Min value of the objective function z = 060x+0.50y is?

    This value is located at?

    B. The max value of the objective function z = 2.25x + 1.25y is?

    The value is located at?

    The min value of the objective function z = 2.25x + 1.25y is?

    This value is located at?

    Thank you in advance!!
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  2. #2
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    Re: The graph to the right shows a region of feasible solutions IMG included

    Quote Originally Posted by Niaboc View Post
    The graph to the right shows a region of feasible solutions. Use this region to find the maximum and minimum values of the given objective functions, and the locations of these values on the graph.

    A. z = 0.60x + 0.50y
    B. z = 2.25x + 1.25y

    Here is a photo of the graph:

    Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting


    A. The max value of the objective function z = 060x + 0.50y is?

    The value is located at?

    The Min value of the objective function z = 060x+0.50y is?

    This value is located at?

    B. The max value of the objective function z = 2.25x + 1.25y is?

    The value is located at?

    The min value of the objective function z = 2.25x + 1.25y is?

    This value is located at?

    Thank you in advance!!
    Judging by how you posted the question, you seem to want us to do the work for you. That is not going to happen.

    x and y will represent quantities of two commodities, and an objective function is a function that we want to maximise or minimise (depending on the context of the question, you might want to maximise profits, or you might want to minimise costs or time taken to complete a project, for example) from these commodities. But this will depend on certain constraints.

    The constraints will be drawn as linear inequalities, which together give a feasible region.

    The most important thing to remember is that linear functions reach their maximum or minimum at their endpoints. The endpoints of these linear inequalities are at the corner points.

    So you need to evaluate the objective functions at each of the corner points (i.e. substitute each corner point into the objective functions), and see which corner points give you the maximum and minimum values, and of course, what those maximum and minimum values are.

    See how you go.
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  3. #3
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: The graph to the right shows a region of feasible solutions IMG included

    Double check these:
    Attached Thumbnails Attached Thumbnails The graph to the right shows a region of feasible solutions IMG included-region-max-min.png  
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