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Worksheet for Example 3 (copy and paste to Google Doc if desired)Marcus is creating a low-fat pie crust recipe for his pie shop.Butter has six (bst) grams of saturated fat and one gram (bpt) of polyunsaturated fat per tablespoon.Vegetable shortening has one (vst) gram of saturated fat and four (vpt) grams of polyunsaturated fat per tablespoon.In the recipe, the butter and vegetable shortening will not be more than 25 (T) tablespoons together.The butter and vegetable shortening combine for at least 34 (sg) grams of saturated fat and at least 44 (pg) grams of polyunsaturated fat. Butter has 100 (bct) calories per tablespoon and vegetable shortening has 115 (vct) calories per tablespoon.Find out what is the best recipe that will minimize the number of calories.----What do we need to do?We need to find how many tablespoons of butter and how many tablespoons of vegetable shortening Marcus should use to minimize the calories ...What are the constraints (limitations)?... and at the same time have no more than 25 T of fat and at least 34 grams of saturated fat and at least 44 grams of polyunsaturated fat.----The first task is to translate the question to the language of equations and we do it by introducing variables:? x= number of tablespoons butter, y= number of tablespoon of shortening.? The rest follows. * The sentence: "the butter and vegetable shortening will not be more than 25 tablespoons together" is translated to x+y<=25We separate the saturated and polyunsaturated fats to get: * Butter has 6 grams of saturated fat and vegetable shortening has 1 gram of saturated fat per tablespoon and all together we want at least 34 grams of saturated fat is translated to: 6x+y>=34?? (bst + vst >= sg).* In the same way, butter has 1 gram of polyunsaturated fat and vegetable shortening has 4 grams of polyunsaturated fat per tablespoon and all together we want at least 44 grams of polyunsaturated fat is translated to x+4y>=44?? (bpt + vpt >= pg).Finally the total number of calories is C=100*x + 115*y? (C= bct*x + vct*y) and we need to minimize this value.Stage 1:? Read the problem several times until you understand it. Note that x>=0 and y>=0 must also be true.Stage 2:? Watch the video:? Stage 3:? Create the GeoGebra worksheet yourself with understanding.Stage 4:? Read the problem again and pretend you are actually doing the recipe.Stage 5:? Complete the following survey (below with sample answer – good for Google survey).TimestampNameDid you watch the movie? How many times?Did you actually do the GeoGebra worksheet yourself?What is the answer to the problem? Remember to include units.Explain in your own words the equation x+4y>=44Explain in your own words the equation C=100*x + 115*yDescribe your overall understanding of the problem, its meaning and the method of solving it.Timestamp1/1/2010 4:17:10NameL.StojanovskaDid you watch the movie? How many times?Yes, 3 times.Did you actually do the GeoGebra worksheet yourself?YesWhat is the answer to the problem? Remember to include units.The minimum calories is 1550kCal when we use 4T of butter and 10T of vegetable shortening.Explain in your own words the equation x+4y>=44These are grams of polyunsaturated fat. Butter has 1 [g/T] and vegetable shortening has 4 [g/T] of polyunsaturated fat. There are x [T] of butter and y [T] of vegetable shortening. The recipe must have at least 44 [g]. So 1 [g/T] * x [T] + 4 [g/T] *y [T] >= 44 [g] . All units are grams! So x+4y>=44.Explain in your own words the equation C=100*x + 115*yThe number of calories C [kCal] from fat is dependent on the number of tablespoons of butter and vegetable shortening. There are 100 [kCal/T] in butter and 115 [kCal/T] in vegetable shortening. There are x [T] of butter and y [T] of vegetable shortening. So C [kCal] = 100 [kCal/T] * x [T] + 115 [kCal/T] *y [T]. All units are kCal! So C=100x+155y.Describe your overall understanding of the problem, its meaning and the method of solving it.1. I liked this problem because it required me to "sort out" the types of fats and different units. Also, I had to think about what my answer needed to be and the correct units, because it was not specifically stated in the problem. I think that checking units is essential to the understanding of any problem and in this problem the meaning only becomes clear when the units are clear. 2. After testing the intersection points I made a slider and a line for Calories and proved that the point G(4,10) does give the minimum calories. 3. I wanted to see what the maximum calories would be so I tested some more and found that the intersection point I gave the maximum of 2848kCal with 1.8 T of butter and 23.2 T of vegetable shortening. ................
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