# calc

posted by on .

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?

• linear programming - ,

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

• whoops - ,

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