After class, you and your fellow Linear Algebra chums decide to make some food.
ID: 2250968 • Letter: A
Question
After class, you and your fellow Linear Algebra chums decide to make some food. You have 12 pounds of butter, 8 cups of sugar, and 16 cups of flour. You also have a recipe book, which consists of exactly five recipes:1
Butter Cookies – each batch takes 2 pounds of butter, 1 cup of sugar, and 2 cups of flour.
Sugar Cookies – each batch takes 2 pounds of butter, 1 cup of sugar, and 2 cups of flour.
Biscuits – each batch takes 1 pound of butter, 1 cup of sugar, and 2 cups of flour.
Flour Pie – each pie takes 2 pounds of butter, 1 cup of sugar, and 3 cups of flour.
Butter Cake – each cake takes 3 pounds of butter, 2 cups of sugar, and 1 cup of flour.
You are not permitted to make fractional batches, cakes, or pies. Assuming you use all of your ingredients, the question is: what combinations of baked goods are possible? Of course, we would allow solutions with, say, no flour pie, but not -3 or 1.4 flour pies.
Explanation / Answer
I have one solution.we can make 4 sugar cookies which will use
4*2=8 butter
4*1=4 sugar
4*2=8 flour
and 4 Biscuits which will use
4*1=4 butter
4*1=4 sugar
4*2=8 flour
and the total of butter is 8+4=12
sugar is 4+4=8
flour is 8+8=16
which is equal to the given quantity.
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