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# Formulate a linear program

Problem:
You work for a food company that makes two types of trail mix: Peak and TrailSnack. Each consists of some mix of peanuts, cashews, and raisins. You can obtain up to 100 kg/day of peanuts, 70 kg/day of cashews, and 60 kg/day of raisins. The Peak mix must contain at least 40% peanuts, at least 20% cashews and at least 20% raisins. The TrailSnack mix must have between 30% and 50% peanuts, and at least 20% cashews and at least 20% raisins. The Peak mixture sells for \$1.80 per 100g and the TrailSnack mix sells for \$1.50 per 100g. Ignoring the costs of the ingredients, formulate a linear program to maximize the revenue from the sales of the two types of trail mix.

Solution and Question:
I know that peak and trailsnack are the main variables in the objective function so I would say z = 18x1 + 15x2 if I am dealing with \$/Kg but in this question x1 and x2 are made from peanuts x3, cashews x4, and raisins x5. I am not sure how to express the rates i.e. kg/day and the constraints i.e. between 30% and 50% with x1 and x2

I only request to formulate the problem. I will try and continue from there.

#### Solution Preview

The solution file is attached.

You work for a food company that makes two types of trail mix: Peak and TrailSnack. Each consists of some mix of peanuts, cashews, and raisins. You can obtain up to 100 kg/day of peanuts, 70 kg/day of cashews, and 60 kg/day of raisins. The Peak mix must contain at least 40% peanuts, at least 20% cashews and at least 20% raisins. The ...

#### Solution Summary

The expert formulates a linear program for Simplex Methods. A Complete, Neat and Step-by-step Solution is provided in the attached file.

\$2.19