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January 31, 2015

Posted by **Jay** on Monday, June 6, 2011 at 6:19pm.

SIMPLEX METHOD - Table:

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!

Math - MathMate, Sunday, June 5, 2011 at 7:07am

You must already have:

x1+x2+x3+x4=10

and

855x1+435x2+1024x3+162x4 < 7000

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

Can you take it from here?

Math - Jay, Monday, June 6, 2011 at 6:15pm

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?

- Math -
**Damon**, Monday, June 6, 2011 at 6:50pmThose are the constraints you were given.

You talk about an answer but have not defined objective yet.

remember maximize carbs

carbs = 31.4 x1 + 114.74 x2 etc

- Math -
**Jay**, Monday, June 6, 2011 at 7:40pmI have the objective, I just need the constraints. If you can please list all of the constraints. The constraint that is stumping me is the one where I have to show 10% of the total. Thanks!!!!!

- Math -
**Jay**, Monday, June 6, 2011 at 7:48pmWhat is the proper constraint for this:

"You want each of the ingredients to contribute at least 10% of the total volume of the mix made."

- Math -
**MathMate**, Tuesday, June 7, 2011 at 7:54amSorry, after re-reading:

"want to make*at most*10 cups of trail mix"

which means that the total weight is not yet known. So

x1+x2+x3+x4=10 does not apply.

Also instead of

x1>1,x2>1....

take the total weight as

W=x1+x2+x3+x4, so the new constraints should be:

x1≤(x1+x2+x3+x4)/10

or simplified to

9x1≤x2+x3+x4

and similarly,

9x2≤x1+x3+x4

9x3≤x1+x2+x4

9x4≤x2+x3+x3

The constraints are now:

855x1+435x2+1024x3+162x4 < 7000

9x1≤x2+x3+x4

9x2≤x1+x3+x4

9x3≤x1+x2+x4

9x4≤x2+x3+x3

x1+x2+x3+x4≤10

Would that work?

- Math - typo -
**MathMate**, Tuesday, June 7, 2011 at 11:50amShould read:

9x4≤x1+x3+x3

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