FarmFresh Foods manufactures a snack mix called TrailTime by blending three ingr
ID: 3222803 • Letter: F
Question
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. 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 1100 calories and no more than 25 grams of fat. Dried fruit must be at least 20% of the volume of the mixture, and nuts must be no more than 25% of the weight of the mixture. Let x = amount (ounces) of dried fruit to put into TrialTime. Let y = amount (ounces) of nut mix to put into TrialTime. Let z = amount (ounces) of cereal mix to put into TrialTime. Develop a model that meets these restrictions to minimizes the cost of the blend. a) What is the objective function? b) What is the constraint for calories? c) What is the constraint for fat? d) What is the volume constraint for dried fruit? e) What is the weight constraint for nut mix?Explanation / Answer
Objective Funtion
Minimize cost = 0.4x + 0.5 y + 0.2z
subject to
Constraints
0.3x + 0.5y + z > 3
0.3x + 0.5y + z < 4
Calorie Constraint
150x + 400y + 50z < 1100
Fat Constraint
0x + 10y + z < 25
Volume constraint of dried fruit
x >= 0.25(x + y + z)
0.75x - 0.25y - 0.25z >= 0
Volume constraint of nut mix
y <= 0.25(x + y + z)
-0.25x + 0.75y - 0.25z <= 0
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