Math, microeconomics

Question

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 226 grams of protein and at least 166 grams of fat. If chicken costs 9¢ per ounce and grain costs 1¢ per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize cost? (If an answer does not exist, enter DNE.)

grain ....... oz

chicken ....... oz

Answer 1

chicken: 10 g protein, 5 g fat per oz

grain: 2 and 2

need 226 and 166

grain cost 1 cent per oz

chicken 9 cents

how much to min cost?

9g+c =cost

10c+2g=226

5c+2g= 166

5c+g= 113

g=166-113= 53 grams grain

c= 12 grams chicken

(53)+(9)12= $1.61 mixture for 226 and 166

33.2)9)= $2.99 all chicken for 332 and 166

113(1)=$1.13 all grain for 226 and 226

use all grain 113 grams