Posted by **liz** on Friday, September 16, 2011 at 3:25am.

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 -
**Damon**, Friday, September 16, 2011 at 7:04am
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 -
**Damon**, Friday, September 16, 2011 at 7:13am
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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