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 1000 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 15% of the weight of the mixture. Develop a model that meets these restrictions and minimizes the cost of the blend.
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.
Let D = number of ounces of dried fruit mix in the blend
N = number of ounces of nut mix in the blend
C = number of ounces of cereal mix in the blend
Min 0.35D + 0.50N + 0.20C
s.t. 0.25D + 0.375N + C ? 3
0.25D + 0.375N + C ? 4
150D + 400N + 50C ? 1000
10N + C ? 25
0.2D ? 0.075N ? 0.2C ? 0
?0.15D + 0.85N ? 0.15C ? 0
D, N, C ? 0
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