Farm Fresh Foods manufactures a snack mix called Trailtime by blending three ingredients: a dried fruit...

 

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Farm Fresh Foods manufactures a snack mix called Trailtime by blending three ingredients: a dried fruit mixture, a nut mixture, and a cereal mixture. Information about the three ingredients (per ounce) is shown below. Min s.t. Ingredient Cost Dried Fruit 0.40 Nut mix Cereal mix Fat Content Minimum Box Size Maximum Box Size Calorie Content Dried Fruit Volume 0.55 Nut Mix Weight X1, X2, X3 20 0.25 Volume Fat Grams 1/4 cup 3/8 cup 1 cup The company needs to develop a linear programming model whose solution would tell them how many ounces of each mix to put into the Trailtime blend. Trailtime is packaged in boxes that will hold between two and three cups. The blend should contain no more than 975 calories and no more than 20 grams of fat. Dried fruit must be at least 20% of the volume of the mixture, and nuts must be no more than 15% of the weight of the mixture. Develop a model that meets these restrictions and minimizes the cost of the blend. (Let X = number of ounces of dried fruit mix in the blend. Let X = number of ounces of nut mix in the blend. Let X3 = number of ounces of cereal mix in the blend.) 0 10 1 Calories 150 400 50 Farm Fresh Foods manufactures a snack mix called Trailtime by blending three ingredients: a dried fruit mixture, a nut mixture, and a cereal mixture. Information about the three ingredients (per ounce) is shown below. Min s.t. Ingredient Cost Dried Fruit 0.40 Nut mix Cereal mix Fat Content Minimum Box Size Maximum Box Size Calorie Content Dried Fruit Volume 0.55 Nut Mix Weight X1, X2, X3 20 0.25 Volume Fat Grams 1/4 cup 3/8 cup 1 cup The company needs to develop a linear programming model whose solution would tell them how many ounces of each mix to put into the Trailtime blend. Trailtime is packaged in boxes that will hold between two and three cups. The blend should contain no more than 975 calories and no more than 20 grams of fat. Dried fruit must be at least 20% of the volume of the mixture, and nuts must be no more than 15% of the weight of the mixture. Develop a model that meets these restrictions and minimizes the cost of the blend. (Let X = number of ounces of dried fruit mix in the blend. Let X = number of ounces of nut mix in the blend. Let X3 = number of ounces of cereal mix in the blend.) 0 10 1 Calories 150 400 50

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To formulate a linear programming model for this problem lets define the decision variables Let x1 b... View the full answer