SOLUTION: Two foods, I and II contain the following percentages of carbohydrates, protein, and fat: Food Carbohydrates Protein Fat I 40%

Question 136872: Two foods, I and II contain the following percentages of carbohydrates, protein, and fat:
Food Carbohydrates Protein Fat
I 40% 50% 6%
II 60% 20% 4%
Food I costs 3c. per gram, and food II costs 4c per gram. Determine the amount of each that should be served to produce at leat 10 grams of carbohydrates, 7.5 grams of protein, and 1.2 grams of fat, if cost is to be minimized.
Let x=amount of food I
Y=amount of food II
minimize z=0.03x + 0.04y, subject to 0.4x+0.6y=10
0.5x +0.2y=7.5
0.06x+0.04y=12
x=0, y=0
How should I draw this and add this formula in excel?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Two foods, I and II contain the following percentages of carbohydrates, protein, and fat:
Food Carbohydrates Protein Fat
I 40% 50% 6%
II 60% 20% 4%
Food I costs 3c. per gram, and food II costs 4c per gram. Determine the amount of each that should be served to produce at least 10 grams of carbohydrates, 7.5 grams of protein, and 1.2 grams of fat, if cost is to be minimized.
Let x=amount of food I
Y=amount of food II
minimize z=0.03x + 0.04y, subject to
carbo:...0.4x+0.6y >=10
Protein: 0.5x +0.2y >=7.5
Fat:....0.06x+0.04y >=12
x>=0, y>=0
How should I draw this and add this formula in excel?
--------------------------------------
Solve each equation/inequality for y and graph it in the 1st Quadrant:
carbo: y >=(-2/3) x + (100/6)
Proten:y>= (-5/2)x+ (75/2)
Fat...: y <= (-3/2)x +300
--------------------------------

Find the points of intersection in the colution area of the three iniequalities.
Test each of those sets of coordinates in the objective equation.
================================
Cheers,
Stan H.

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