Nutrition Ruff, Inc. makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 224 grams of protein and at least 174 grams of fat. If chicken costs 11 per ounce and grain costs 2 per ounce, how many ounces of each should Ruff use in each bag of dog food in order to minimize cost?

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  1. a) 10 c + 2 g >/= 224
    b) 5 c + 2 g >/= 174

    c) minimize p = 11 c + 2 g

    graphs c on x axis, g on y
    a) (0,112) (22.4,0)
    b) (0,87) (34.8,0)
    intersection of lines a and b
    10 c + 2 g = 224
    10 c + 4 g = 348
    -2 g = -124
    g = 62
    then c = 10
    so (10,62)

    cost line p = 11 c + 2 g
    check corners (0,87)(10,62)(12.4,0)
    first p = 2*87 = 174
    second p = 110+124 = 234
    third p = 11*12.4 = 136.4
    so I get all chicken

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  2. whoops, need to be above and to the right of the lines so corners are
    (0,112) (34.8, 0) (10,62)
    first 2*112= 224
    second 234 again
    third 11*34.8 = 382.8
    so I get all grain

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