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Mathematics

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Suppose a, b, c are nonnegative numbers, and 3a + 2b + c = 5, 2a + b − 3c = 1. Find the Maximum value of S = 3a + b − 7c.

  • Mathematics - ,

    Do you know linear programming?
    draw 3 axis graph (x,y,z) is (a, b , c)
    Find all the corners of (a,b,c)
    when a = 0
    (0,0,5) (0,5/2,0)
    and
    (0 , 0 , -1/3) (0 1, 0)

    when b = 0
    (0,0,5) ( 5/3,0,0)
    and
    (1/2,0,0) (0,0,-1/3) note negative

    when c = 0
    (0,5/2,0) ( 5/3,0,0)
    and
    (0,1,0) (1/2,0,0)

    You have three likely corners
    p (5/3, 0, 0)
    q (0, 5/2, 0)
    r (0, 0, 5 )
    try
    p
    S = 5
    try q
    S = 5/2
    try r
    S = negative
    so the biggest I got was 5

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