Ruff, Inc. makes dog food out of chicken and grain. Chicken has 10 grams of prot

Question

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 216 grams of protein and at least l76 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 in order to minimize cost? Grain oz chicken oz The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 760 homeless patients and no more than 1,000 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 2, 400 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $7, 600 per month. How many of each type of patient should it house in order to maximize profit? high-income patients homeless patients profit $

Explanation / Answer

Let x ounces be the chicken and y ounces be the grain required for the dog food.

As per given question we can formulate the LPP as below

Minimize Z = 9x + y

subject to,

10x + 2y >=216

5x + 2y >= 176

x >= 0, y >= 0

Solving this, we have x = 0 and y =108

This means grain 108 oz and chicken 0 oz

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