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December 10th, 2010, 01:37 PM   #1
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Help setting up matrix from this word problem????

I'm trying to follow along in the book but can't seem to get my head around how to solve this one. Could someone help me to setup of the equation from this?

The problem:

A nutritionist attached to the University, has been asked to prepare special diets for two patients, Lauren and Bill. The nutritionist has decided that Lauren's meals should contain at least 300mg of calcium, 15mg of iron, and 40mg of vitamin c, and Bill's should contain 400mg calcium, 15mg iron, and 50mg vitamin c. The nutrionist has decided that the meals are to be prepared from three basic foods: A, B, and C. The nutritional contents of these foods are summarized in the table below. Find how many ounces of each type of food should be used in a meal so that the minimum requirements of calcium, iron, and vitamin c are met for each patient.

Food A = 35mg calcium, 1mg iron, 3mg vitamin c
Food B= 30mg cal, 1mg iron, 5mg vit c
Food C = 15mg cal, 2mg iron, 4mg vit c

Could someone help me setup the matrix for the equation? I'm stumped and have no idea where to even start. Thanks.
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December 10th, 2010, 09:04 PM   #2
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Re: Help setting up matrix from this word problem????

Imagine three variables: a, b, and c, where a is the amount of A, etc.

Then I have the following equations for the first patient:

35a +30b +15c > 300
a + b + 5c > 15
3a + 5b + 4c > 40.

Do you see how to turn this into a matrix?
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December 11th, 2010, 12:26 PM   #3
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Re: Help setting up matrix from this word problem????

Yes THANK YOU!!!!!! I had a feeling once I saw it, it would be a moment.
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December 11th, 2010, 03:26 PM   #4
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Re: Help setting up matrix from this word problem????

Very good! It happens to everyone from time to time. Good luck.
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