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.
A Complete, Neat and Step-by-step Solution is provided in the attached file.