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Math Help - Simplex method, confused with how to set up.

  1. #1
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    Simplex method, confused with how to set up.

    The XYZ Corporation plans to open three different types of fast food restaurants. Type A restaurants require and initial cash outlay of $600,000, need 15 employees and are expected to make an annual profit of $40,000. Type B restaurants require an initial outlay of $400,000, need 9 employees and are expected to make an annual profit of $30,000. Type C restaurants require an initial outlay of $300,000, need 5 employees, and are expected to make an annual profit of $25,000. The XYZ Corporation has $48,000,000 available for initial outlays, does not want to hire more than 1000 new employees, and would like to open 70 restaurants. How many restaurants of each type should be opened to maximize the expected annual profits? Set up your Simplex Tableau using units of $1000.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by drh890 View Post
    The XYZ Corporation plans to open three different types of fast food restaurants. Type A restaurants require and initial cash outlay of $600,000, need 15 employees and are expected to make an annual profit of $40,000. Type B restaurants require an initial outlay of $400,000, need 9 employees and are expected to make an annual profit of $30,000. Type C restaurants require an initial outlay of $300,000, need 5 employees, and are expected to make an annual profit of $25,000. The XYZ Corporation has $48,000,000 available for initial outlays, does not want to hire more than 1000 new employees, and would like to open 70 restaurants. How many restaurants of each type should be opened to maximize the expected annual profits? Set up your Simplex Tableau using units of $1000.
    Introduce variables for the number of type A, B and C resturants I would call these A, B and C but your course may favour x_1, x_2 and x_3.

    Now write the constraints, you have an outlay constraint, an employee constraint, and a total number constraint as well as the usual non-negativity constraints.

    The objective to maximise is the total anual profit.

    CB
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  3. #3
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    thanks

    i stared at that problem for a little while without a clue where to start. i think i have it now though. thanks for the advice tho, it really helped give me an idea on how to sort it out.

    thanks
    ~Dale.
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