Explore BrainMass

Explore BrainMass

    Linear Programming : Simplex Method

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    1. Consider the simplex tableau

    x y u v w M
    [ 1 0 3 0 0 0 | 10]
    [ 0 0 1 0 1 0 | 0]
    [ 0 1 -6 0 0 0 | 3]
    [ 0 0 8 1 0 0 | 7]
    [ 0 0 5 0 0 1 4]

    The tableau above is the final one in a problem to minimize -x + 2y. The minimum value of -x + 2y is:

    a. -10
    b. -4
    c. 0
    d. 4
    e. none of the above

    2. The inequality 2x - y + 5z (greater than or equal to symbol) -6 is equivalent to the inequality

    a. 2x - y + 5z (less than or equal to symbol) -6
    b. 2x - y + 5z (greater than or equal to symbol) 6
    c. -2x + y - 5z (less than or equal to symbol) -6
    d. -2x + y -5z (greater than or equal to symbol) 6
    e. none of the above

    3. Consider the following linear programming problem: A workshop of Peter's Potters makes vases and pitchers. Profit on a vase is $3; profit on a pitcher is $4. 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
    [ -1 1 1 0 0 | 4 ]
    [ 2 | ]
    [ 1 1 0 1 0 | 6 ]
    [-3 -4 0 0 1 | 0 ]
    (initial)

    x y u v M
    [ 0 1 2 -1 0 | 2 ]
    [ 1 0 -2 2 0 | 4 ]
    [0 0 2 2 1 | 20 ]
    (final)

    If kiln time were decreased by one unit per day, determine the optimal performance schedule.

    a. x = 3, y = 4
    b. x = 4, y = 2
    c. x = 6, y = 1
    d. x = 2, y = 3
    e. none of the above

    4. In a linear programming problem in a standard from, the initial and final tableaux are given as below:

    x y u v M
    [ 1 3 1 0 0 | 50 ]
    [ 1 5 0 1 0 | 70 ]
    [-6 -24 0 0 1 | 0 ]
    (initial)

    x y u v M
    [ 0 1 2 -5 -3 | 20 ]
    2 2
    -1 1
    [ 1 0 2 2 0 | 10 ]
    [0 0 3 3 1 | 360]
    (final)

    Given that x (greater than or equal to sign) 0 and y (greater than or equal to sign) 0, if h units were added to the first resource, the maximum value of the objective function is

    a. 360
    b. 360 + 3h
    c. 360 + h
    d. 360 + h(to the 5th power)/2
    e. none of the above

    5. To solve the linear programming problem

    Minimize 50x + 70y subject to:

    x + y (greater than or equal to symbol) 6
    3x + 5y (greater than or equal to symbol) 24 we can use the simplex method on its dual.
    x (greater than or equal to symbol) 0 , y (greater than or equal to symbol) 0
    The objective function of the dual is

    a. u + 3v
    b. u + 5v
    c. 6u + 24v
    d. 70u + 50v
    e. none of the above

    © BrainMass Inc. brainmass.com March 4, 2021, 6:14 pm ad1c9bdddf
    https://brainmass.com/math/linear-programming/linear-programming-simplex-method-35911

    Attachments

    Solution Summary

    The simplex method is investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

    $2.49

    ADVERTISEMENT