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Wednesday, October 14, 2009
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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 220 grams of protein and
at least 150 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?
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You are thinking of making your mansion more energy efficient
by replacing some of the light bulbs with compact fluorescent
bulbs, and insulating part or all of your exterior walls. Each
compact fluorescent light bulb costs $4 and saves you an
average of $2 per year in energy costs, and each square foot of
wall insulation costs $1 and saves you an average of $0.20 per
year in energy costs. Your mansion has 250 light fittings and
3100 sq. ft. of uninsulated exterior wall. To impress your
friends, you would like to spend as much as possible, but save
no more than $800 per year in energy costs (you are proud of
your large utility bills). How many compact fluorescent light
bulbs and how many square feet of insulation should you
purchase? How much will you save in energy costs per year?
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The Megabuck Hospital Corp. is to build a state-subsidized
nursing home catering to homeless patients as well as highincome patients. State regulations require that every subsidized
nursing home must house a minimum of 750 homeless patients
and no more than 1000 high-income patients in order to qualify
for state subsidies. The overall capacity of the hospital is to be
2400 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 $9900 per month for every homeless patient it
houses, whereas the profit per high-income patient is estimated
at $7600 per month. How many of each type of patient should it
house in order to maximize profit?
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