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    Linear Programming and the Simplex methods : Surpluses

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    Consider the following linear programming problem: A workshop of Peter's Potters makes vases and pitchers. Profit on a vase is $3.00; profit on a pitcher is $4.00. Each vase requires ½ hour of labor, each pitcher requires 1 hour of labor. Each item requires 1 unit of time in the kiln. Labor is limited to 4 hours per day and kiln time is limited to 6 units per day. Initial and final tableaux are shown in finding the production plan which will maximize profits: (x = number of vases and y = number of pitchers made per day).

    X y u v M x y u v M
    ½ 1 1 0 0 4 0 1 2 -1 0 2
    1 1 0 1 0 6 1 0 -2 2 0 4
    -3 -4 0 0 1 0 0 0 2 2 1 20

    (initial) ( final)

    How much surplus labor is there when the optimal plan is in effect?

    a. 0 hours
    b. 2 hours
    c. 4 hours
    d. 1 hour
    e. None of the above

    If labor were increased by one hour a day, profits could be increased to:

    a. $24
    b. $22
    c. $21
    d. Not increased
    e. None of the above

    If labor were increased by one hour a day, the optimal production plan would require how many vases?

    a. 2
    b. 3
    c. 4
    d. 1
    e. None of the above

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    https://brainmass.com/math/linear-programming/linear-programming-simplex-methods-surpluses-44980

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    Consider the following linear programming problem: A workshop of Peter's Potters makes vases and pitchers. Profit on a vase is $3.00; profit on a pitcher is $4.00. Each vase requires ½ hour of labor, each pitcher requires 1 hour of labor. Each item requires 1 unit of time in the kiln. Labor is limited to 4 hours per day and kiln time is limited to 6 units per day. Initial and final ...

    Solution Summary

    Linear programming and the simplex methods for analyzed. The surpluses of pitchers are computed.

    $2.49

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