Assignment:
Dugie Hansen is an elementary school teacher who also raise guinea pigs for supplemental income. He is trying to decide what to feed his pigs. He is considering using a combination of two popular guinea pig foods from the local pet store: Kaytee Fiesta Gourmet Diet and Oxbow Essentials Cavy Diet. He would like to feed the guinea pigs at a minimum cost while also making sure that each animal receives an adequate supply of calories and vitamins. The cost, calorie content and vitamin content of each feed is given in the table below.
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Kaytee Fiesta
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Oxbow Essentials
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|
Calories (per pound)
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80
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100
|
|
Vitamins (per pound)
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14 units
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7 units
|
|
Cost (per pound)
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$1.40
|
$1.80
|
|
|
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Each guinea pig requires at least 800 calories per day and at least 70 units of vitamins. An additional constraint is that no more than 30% of the diet (by weight) can consist of Kaytee Fiesta, since it contains an ingredient that is toxic if consumed in too large a quantity.
Required:
Question: Write the linear programming formulation to help Dugie determine how much of each feed he should give to the guinea pigs daily.