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 11¢ 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? HINT [See Example 4.] (If an answer does not exist, enter DNE.)

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Dryomys Dryomys · Answer 1 · 2019-09-19T10:47:53+02:00

Answer: Ruff, Inc., should use 0 oz of chicken and 113 oz grain.

Explanation:

Given that,

Chicken:

10 grams of protein

5 grams of fat per ounce

Grain:

2 grams of protein

2 grams of fat per ounce

Chicken costs = 11¢ per ounce

Grain costs = 1¢ per ounce

Let x be chicken and y be grain

Objective is to minimize 11x +y

subject to

10x +2y ≥ 226

5x + 2y ≥ 166

Solving these two equations, we get,

point (1)- (12, 53) and two corner solution

(2)- (0,113)

(3)- (33.2,0)

Price of 1) = 12 × 11 + 53 × 1 = 185

Price of 2) = 0 ×11 + 113 × 1 = 113

Price of 3) = 33.2 × 11 + 0 × 1 = 365.2

Therefore, Ruff, Inc., should use 0 oz of chicken and 113 oz grain.