Nutrient Peanuts Raisins M&Ms Pretzels
Calories 855 435 1024 162
Protein 34.57 4.67 9.01 3.87
Fat 72.50 0.67 43.95 1.49
Carbs 31.40 114.74 148.12 33.68

Suppose that you want to make at most 10 cups of trail mix, using all the ingredients. You want each of the ingredients to contribute at least 10% of the total volume of the mix made. You want the entire amount of trail mix to have fewer than 7000 calories and you want to maximize the amount of carbs in the mix.

1. Let x1 be the number of cups of peanuts, x2 cups of raisins, x3 cups of m&ms and x4 cups of pretzels. Let C be the amount of carbs in the mix. Find the objective function.
2. What contraints must be placed on the objective function.

I can solve the rest if you can help out with the constraints. I'm not sure how to write out the 10% of each ingredient to a proper constraint. Thanks!

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  1. You must already have:
    855x1+435x2+1024x3+162x4 < 7000

    The total volume is 10 cups, what is 10% of 10 cups?

    Can you take it from here?

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  2. MathMate,
    Sorry.. still confused. I set up the constraints as x1>1, x2>1, x3>1, x4>1 but I'm not getting the answer. Are those contraints correct or is there another way to write it?

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