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# optimal solution

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 Fruit .35 .25 cup 0 150
Nut Mix .50 .375 cup 10 400
Cereal Mix .20 1 cup 1 50

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, using MS, Excel Solver, or an online LP solver. What is the optimal solution, that is, how much does a box cost, and how many ounces of each ingredient does it contain?

#### Solution Preview

Please consult the accompanying Excel spreadsheet for the solver setup.

I put the weights of each ingredient in cells B2:4 and summed them up in B5. Columns C-F represent the other table entries with row 5 showing a total for each column. We also have to set up % volume of dried fruit and % weight of nuts. D9 is volume of nuts/volume of all ingredients and D12 is weight of nuts / total weight. Now we can set up the ...

#### Solution Summary

THis solution determines the optimal solution, that is, how much does a box cost, and how many ounces of each ingredient does it contain?

\$2.19