Linear Algebra One serving of Lucky Charms contains 10% of the percent daily val

Question

Linear Algebra

One serving of Lucky Charms contains 10% of the percent daily values (PDV) for calcium, 25% of the PDV for iron, and 25% of the PDV for zinc. One serving of Raisin Bran contains 2% of the PDV for calcium, 25% of the PDV for iron, and 10% of the PDV for zinc. Determine the number of servings of each cereal required to get the given mix of nutrients.

58% of the PDV for calcium, 225% of the PDV for iron, and 165% of the PDV for zinc.

Lucky Charms     servings Raisin Bran     servings

Explanation / Answer

First tabulate the information given and required.

Also x >0 and y>0

Graph shows as below

First two equations give x =5 and y = 4

Thus solutions can be (5,4) ((9,0) (0,29)

Calcium Iron Zinc Total (in percents) Lucky charms 10 25 25 60 Raisin Bran 2 25 10 37 Reqd 58 225 165 10x+2y > 58 25x+25y > 225 25x+10y >165

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