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Minimize z = 3x + 6y subject to:
4x + y ? 20
x + y ? 20
x + y ? 10
x ? 0
y ? 0 
Graph the feasibility region.
Identify all applicable corner points of the feasibility region.
Find the point(s) (x,y) that minimizes the objective function z = 3x + 6y.

  • math -

    I assume those ? marks are < and > marks

    corners
    (0,0)

    4x+y = 20
    if x = 0, y = 20
    if y = 0, x = 5

    x+y = 20
    if x = 0 , y = 20
    if y = 0 , x = 20
    this one is above and beyond the others when you graph it

    x+y = 10
    if x = 0 , y = 10
    if y = 0, x = 10

    intersection of
    x+y = 10
    4x+y = 20
    ---------
    -3 x = -10
    x = 10/3
    y = 7/3

    graph those and you will see that (0,0) is the minimum of 3x+6y

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