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Math Help - I need help finding constraints for this word problem for math

  1. #1
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    I need help finding constraints for this word problem for math

    the dogs in kens k-9 kennel must get at least 40 pounds of food per day. the food may be a mixture of foods x and y. food x has 1 unt per pound of nutrient a and 1/2 unit per pound of nutrient b. food y has 1/3 unit per pound of nutrient a and 1 unit per pound of nutrient b. the daily diet must include at peast 20 units of nutrient A and at least 30 units of nutrient b. the dogs must not get more than 100 pounds of food per day. food x costs $.80 per pound and food y costs $.40 per pound. what is the least possible cost per day for feeding the dogs?
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  2. #2
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    Re: I need help finding constraints for this word problem for math

    Fix units of: pounds for weight, dollars for money, and "units of nutrients" for nutrients.

    Let u = number pounds of food x, and v = number of pounds of food y.
    Let a = units of nutrient A received, and b = units of nutrient B received.
    Let C = daily cost in dollars of feeding a dog.

    "get at least 40 pounds of food per day" becomes:
    u+v>=40.

    "food x has 1 unt per pound of nutrient a and 1/2 unit per pound of nutrient b. y has 1/3 unit per pound of nutrient a and 1 unit per pound of nutrient b" becomes:
    a = (1)u + (1/3)v
    b = (1/2)u + (1)v

    "the daily diet must include at peast 20 units of nutrient A and at least 30 units of nutrient b" becomes:
    a >= 20
    b >= 30

    "the dogs must not get more than 100 pounds of food per day." becomes:
    u+v <= 100

    "food x costs $.80 per pound and food y costs $.40 per pound" becomes:
    C = (4/5)u + (2/5)v

    "what is the least possible cost per day for feeding the dogs?" becomes:
    Minimize C subject to all those constraints.

    Implicit constraints:
    u>=0, v>=0

    Putting it all together:
    u>=0, v>=0
    u+v>=40.
    a = (1)u + (1/3)v
    b = (1/2)u + (1)v
    a >= 20
    b >= 30
    u+v <= 100
    C = (4/5)u + (2/5)v
    Minimize C subject to all those constraints.

    Problem Translated:
    (1)u + (1/3)v >=20
    (1/2)u + (1)v >=30
    u>=0, v>=0
    40<= u+v <= 100
    C = (4/5)u + (2/5)v
    Minimize C subject to all those constraints.
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