FarmFresh 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. ingredient cost volume fat grams calories dried nut .40 1/4 cup 0 160 nut mix .60 3/8 cup 9 390 cereal mix .25 1 cup 2 60 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 three and four cups. The blend should contain no more than 1,100 calories and no more than 30 grams of fat. Dried fruit must be at least 25% of the volume (in cups) of the mixture, and nuts must be no more than 20% of the weight (in ounces) of the mixture. Develop a linear program for this problem that minimizes the cost of the blend and meets all the stated requirements.
FarmFresh 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.
| ingredient | cost | volume | fat grams | calories |
| dried nut | .40 | 1/4 cup | 0 | 160 |
| nut mix | .60 | 3/8 cup | 9 | 390 |
| cereal mix | .25 | 1 cup | 2 | 60 |
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 three and four cups. The blend should contain no more than 1,100 calories and no more than 30 grams of fat. Dried fruit must be at least 25% of the volume (in cups) of the mixture, and nuts must be no more than 20% of the weight (in ounces) of the mixture.
Develop a linear program for this problem that minimizes the cost of the blend and meets all the stated requirements.
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