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celi asked in Science & MathematicsMathematics · 10 months ago

Please help with this math?

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  • Mike G
    Lv 7
    10 months ago

    Max = 6*4+8*8 = 88

    Min = 6*1+8*1 = 14

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  • Obviously, the further to the right we go and the further up we go, the greater the value will be. The further left and further down we go, the smaller the value will be

    6 * 1 + 8 * 1 = 6 + 8 = 14

    The minimum value occurs at (1 , 1) and it's 14.

    The maximum value will occur somewhere along the right-most border. So what we need to do is relate x to y and use a substitution to figure out where the maximum value occurs

    x = 4 , y = 8

    x = 5 , y = 2

    (2 - 8) / (5 - 4) = -6/1 = -6

    We need a line with a slope of -6 that passes through (4 , 8)

    y - 8 = -6 * (x - 4)

    y = 8 - 6 * (x - 4)

    y = 8 - 6x + 24

    y = 32 - 6x

    f(x , y) = 6x + 8y

    f(x , y) = 6x + 8 * (32 - 6x)

    f(x , y) = 6x + 256 - 48x

    f(x , y) = 256 - 42x

    x is bounded between 4 and 5, so 256 - 42 * 4 will give us the greatest value of f(x , y)

    256 - 42 * 4 = 256 - 168 = 88

    Maximum value is 88

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  • 10 months ago

    max = 6*4 + 8*8 = 100

    min = 6*1 + 8*1 = 14

    • Alan
      Lv 7
      10 months agoReport

      Math typo
      6*4= 24
      8*8= 64
      24 + 64 = 88 (not 100)

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