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You’re watching someone’s dog, but sadly they forgot to give youthe dog food. There’s a store nearby that offers four differentsize bags of dog...

Question

You’re watching someone’s dog, but sadly they forgot to give youthe dog food. There’s a store nearby that offers four differentsize bags of dog food. 5lbs at $1.40/lb, 7.5lbs at $1.60/lb, 10lbsat $1.10/lb, and 12lbs at $0.94/lb. The dog is staying with you for7 days and eats three 1/4 lb meals per day. You don’t have a dog soassuming all leftover dog food is wasted, what size bag should youbuy to feed the dog while spending the least amount of money?

You’re watching someone’s dog, but sadly they forgot to give you the dog food. There’s a store nearby that offers four different size bags of dog food. 5lbs at $1.40/lb, 7.5lbs at $1.60/lb, 10lbs at $1.10/lb, and 12lbs at $0.94/lb. The dog is staying with you for 7 days and eats three 1/4 lb meals per day. You don’t have a dog so assuming all leftover dog food is wasted, what size bag should you buy to feed the dog while spending the least amount of money?



Answers

Animal Nutrition Kevin's dog Amadeus likes two kinds of canned dog food. Gourmet Dog costs 40 cents a can and has 20 units of a vitamin complex; the calorie content is 75 calories. Chow Hound costs 32 cents a can and has 35 units of vitamins and 50 calories. Kevin likes Amadeus to have at least 1175 units of vitamins a month and at least 2375 calories during the same time period. Kevin has space to store only 60 cans of dog food at a time. How much of each kind of dog food should Kevin buy each month to minimize his cost?

So for this question, an animal shelter makes its two brands of dog food. So we have brand X and brand. Why, right? X m burn wife on brand X cost $25 for back and contains Come back UN contains So units of nutritional elements a two units of regional elements be so he has so units off a yes. Two units off elements Be yes, two units of elements C right. And now brand. Why cost $20 per bag right on it contains one unit off elements A contains nine units off elements be on three units over elements C now the minimum required amount for no trace A, B and C ah, 12 units. So for eight, the minimum required amount is 12 units for be the minimum requirement. But for me is 36 Units I foresee is 24 years now. What is the optimal number of bags of each brands? That should be mixed on what is the optimal cost. So we need to find the optimal way for making the two brands X and y as food so that the minimum requirements for nutrition is which is this the minimum required Mexes met on. Also, the cost is optimal, so that's what we're trying to do. So let X speak. Number of runs off X on. Why building number bags off? Why? So let's more eggs. Be number of bags of rent X now Why be box of round? Why now? Therefore, the function is going to be C is a quote to 25. Close 20 right? I'm sorry, 25 x was 20 way, and that's because it's 25 for you need off eggs and 20 units $2020 per units for why? So that's that we have to find a minimal cost now on the three constraints can be converted into linear inequalities as two experts. Why is Quintana equal to 12? Because if you go back, we can see that we want to. Units of a four x one is of a for why, and then we want the minimum is 12. So it has to be greater and swelled. So I'm gonna follow that same structure and creates three linear inequalities. So it's going to be the next one is going to be two X was nine way greater than equals to 36 the last one is gonna be two x was three y. Lieutenant equals to 24. Now, this this is a number of bucks used kind of a b negative. So we cannot get more constraints of eggs with 10 and zero and white with another, because with an unequal necessary, because the number of bucks can never be negative. Right? So Well, we know my good to find the Adriatic timing by the constraints on. Then we can see that if you draw the area to tell me by area determined by the constraints. So these are the constituents. Where am I gonna find area as determined by the class drinks? So the time you should look like this. Well, why Over here? Yeah. So, yeah, the first point will be zero. Come on. Four, then. Zero comma. Eighth zero comma 12. They were gonna have a point here on four on four coma for on the point on three. Comma six. This is a Then this points joins to this away. Then this point joins all the way to this one too. So that should look like this. And then we have six trauma zero. Then we have 12 from a zero. No, we have 18 comma. Zero. So we kind of all these points? No. The point on Ni Komatsu and this is point B. So I'm going to connect the point. This is to expose nine. Y is equal to 36. This point is two x close three y Is it called 24 and this is two eggs. What's wise invoices? So this is what this is the area determined by the classrooms. And this is what it looks like on a graph. So they are moving on now. The figure. All right. We can tell that the point is the point Where lines one on three Inter set. If you go back to the table to the they had questions, inequalities, dishes. It is a plane with on one and 3 to 6. So because this is a question three and this is a question one. So if you go back there, we can see that that's when they eight or six a on from equation one two X is equal to to actually cause the 12 minus. Why? So make this work patients to sorry equation for Because if you go up to the graph. This is the question one, this integration suit in question. Three. Rhetta on this situation to. So this point is where the intersect this to the Intersect, So that's official. One. So from equation 12 x right is equal to 12 minus y, and that's Equation four. Now from Equation three two. X equals toward 24 minus three y And that's equation. Would five. Now, at this subsection points X values at the same so we can equate, you know, equals show four on five together so we can get, um, 12 minus. Why is it close to 24? Minus three way then, even though bring it over to the other side, it will be It will be, you know, 12 minus 24 is equal to minus three y plus y and then minus 24 minus 20 No minus 12 and the courts and minus two y and they were divided. Why is he quotes? What six. So you're going to substitute? Why is the course of six in a Christian for so what you thought it serves us See question for we get two X equals 12 minus six x the quote six or what? I'm sorry. Extra cost of three because we divide six. Fight about two. So So now we know what X is, you know, a wise. So the coordinates off the intersection points A is worth three commerce sticks. Now the points be in that is this protection off two or three. You go there. Business and sectional words. So three. So now we can see that from equation too. Confusion, too. We can see that two x is equal to 3. 36 minus nine y And this equation six from aggression three two eggs because 24 minus three wide. That's the question seven. Now intercepting the points. Um, since X values are the same words because, see, six because is seven. So that's six minutes. Nine wise, of course, it's 24 minus three white. Right, So we're going to get that's six minus 24 is, of course, 93 wide close nine wife and then that's it for 24 is 12 on, then its request to six way. And why is it close to two? So because you know why is supposed to subsidies value any question six, which is that so from there to exit goes to take six minus nine times two. I meant to actually supposed to get the six minus spacing and then X is equal to exit. Wants to actually wants to 18. And it X is, of course, tonight so that the body of knife So the coordinates off the point that's a short points off a is my comments to so moving on. We found the coordinates right on at 5. 36 of the region formed by the constraints. The function who have values as following. So at zero comma, 12 Sesay courses 25 open bracket zero was 20 couple of records. Why is what's wolf on? This is going to give it support. See at the 0.3 Commerce six I 0.3 from my sixties it close to 25. Open back at three lost 20 open records. Six on this is 1 95. So this is the minimum while you off See And then my at my Komatsu C is because the 25 open work in nine was 20 open brackets to on this is to 65. I have 18 comma zero Sesay close to 25 open brackets. Kate's name close 20. Open bracket zero on this is the course of 4. 15. So if you look at see what this really well volumes see, and this is the maximum value of C zero. So if we can conclude that the minimum cost, of course, when you know there are three bucks of eggs on six bucks of white, a bolt element Marcoses wanted to five and then the maximum cost, which is this off course. When they're 18 bugs off, it's in box off. It's Andrew Bugs. And what? But you want to find the optimal cost. So the optimal cost cost is nice. 1 95 on it, of course, with three buds off s and six bucks and white. So Dr Marcos is 1 95. The news. Your clothes roots. Three bucks. Oh, it's wild on six bugs off, wife. That's the answer.

What's up, stat cuts. My name is Aaron, and in this video we're gonna be looking at an experiment and discussing some aspects about the design. So a dog food company wants to compare a new, lower calorie food with their standard dog food to see if it's effective in helping inactive dogs maintain a healthy weight. They have found several dog owners willing to participate in the trial. The dogs have been classified a small, medium or large breeds, and the company will supply some owners of each size of dog with one of the two foods. The owners have agreed not to feed their dogs anything else for a period of six months, after which the Dogs weeks will be checked. So the first thing that want to do is I d the treatments, experimental units and the response variable. Then we're going to describe a method of assigning treatments if we're gonna use a block design, and then we're gonna talk about blinding a little bit. So basically, the dog food company wants to test its lower calorie dog food. Um, it's going to give that lower calorie dog food or regular food to dog owners have either small, medium or large breeds, and then they're gonna weigh the dogs after six months. So our first first thing we want to do is we want idea or treatments are experimental units and our response variable. So experimental units are the individuals that were experimenting on. So those were the dogs, and our response variable is our dependent variable. So we manipulate our independent variable toe look for the response and our dependent variable. So what does the company want to know? Well, they want to know if they're lower calorie dog food can help the dogs maintain a healthy weight. So the dogs weight is our dependent variable. And then for our treatments, I just have a little table set up for some visual organization. So I'm gonna put the dogs right here. So we're experimenting on all the dogs, and then they can either have low calorie food or regular. So for our treatments, the dogs can get So for the first treatment, the dogs can have low calorie food. And for the second treatment, the dogs can have regular food. So our treatments are gonna be dogs with low calorie food and dogs with the regular food because these are the two. These are the two conditions were trying to get characteristics on. So Part B is describe a method of assigning treatments if we use a block design by size, so remember we had a choice in the beginning. Said company was gonna give dog food to dog owners that have either small, medium or large dogs. So again, let's do a little visual organization to figure out what kind of treatments we're gonna have. So I'm gonna put small dogs here, medium here and large here again. They're still all dogs. And then we'll just put the low calorie food regular food here again. And then let's count how many treatments we're gonna have. 123 456 So our treatments are gonna be small dogs with low calorie food, small dogs with regular food, medium dogs with low calorie food, medium dogs with regular food, large dogs with low calorie food, and large dogs with regular food. So that would be how we would design our treatments if we were gonna block by size of the dogs. And last thing we're going to talk about is blinding important, so blinding is definitely important in experiments. It helps us avoid bias and get accurate and precise results. So, yeah, blinding is definitely important, Especially if you think about this is a company testing its own product. So there's a lot of conflict of interests there alone. Double blinding, I would say, would definitely be useful in this situation. How could we design with blinding? So we want to do single blinding. We could do something like So we want to do single blind and the company is going to distribute food. Then we could do single blind with the dog owners so we can tell we can not tell dog owners what kind of food they're getting. And this would be useful because if the dog owner knows what type of food they're getting, they might feed the dog differently. So if I know I'm gonna get a low calorie food for my dog and all my poor dog is acting like its hungry and I give it more food, that is conflict of interest that's gonna cause bias in study, because I know what type of food I'm gonna give my dog. So for double blinding, that's when neither the dog owner nor the company would know what kind of food. So so if we wanted to do double blind, we could have neither the dog owners nor the evaluators know what kind of food the dog is getting. And I think that would be the best in this case, considering it's a company testing its own product. And if those researchers are hired by the company to value product, then they have a conflict of interest. If they're hired by that company, they're getting a salary from the company. They want that company to be successful. So this is how I would design with a single binding and double blinding, and I definitely think it would be useful in this experiment. So all right, that was our video. We looked at this dog food example, and we discussed treatments, experimental units and our response variable, as well as describing a method of designing, assigning treatments if we wanted to use a block design. And then lastly, we talked about blinding. Alright, guys, hope you enjoyed it next time

All right. This question gives us a lot of information, so let's just write it down as we read through. So what we're gonna need is an objective function, which is our price. So it tells us that our price they were spending on these bags is $25 per x, plus $20 per y. Then we want our constraints on the nutrients. So, nutrient, eh? We get two units for every X plus one unit for every why, and that has to be bigger and 12. Then for nutrients, be each bag of ex gets too, and each bag off. Why gets nine in the minimum for that has to be 36 and then for C bag Ex has to in bag. Why has three and that's 24 needed, and some or constraints is that you can't have negative bags of dog food. So we're trying to maximize Sorry, minimize the price spent because we're looking for greater than for all these colored lines. So that means that are feasible. Region is anything in here, so it's unbounded, right? Because you could just buy 1000 bags of each food and be set. But for a minimize. Er, what we're looking for is thes vergis, ese. So there's only two options that really work for us in these points are 92 and 36 So let's test the price at each of these and see which one is better. So see of 36 is equal to 25 times three plus 20 times six and punching that into our calculator. We get 1 95 then to test our other point. See of 92 is equal to 25 times nine plus 20 times two, which gives us to 65. So significant difference. So this one is the cheaper option. So minimum price is equal to 1 95 and you want X to be equal to three and why to be equal to six. And this is the solution to our optimization problem.

Hair in this problem if we have to find the weight off Kasandra May me and Midzi Onda were given that when they Cassandra, Mimi and Mitzi V 1 70 wife Bones and Cassandra and make me rich 1 £43 on Cassandra and Midzi weights 1 £39. So there is you, Doctor. The weight off Cassandra, as he calls toe expound on the Adolf Mini is equals to white pounds on the weight off McGee is it calls to Z pounds. So we're given that the value of X plus y plus Z is equals to 1 £75 on Cassandra and mean, that means explain why is given as 1 43 and vie Pless z is given us one party night. Let this be as equation one equation to an equation. Tree now will be using clamors through to find the solution of this equation. And we know that from Clemens through the value of X is the X divided by B really off. Why is divided by the body and the value of Z is the Z divided by d so foster fall will kill credibility off D so d is equals to the regiment. VALUE off 110 111 101 Averaging a coefficient of X in the first column coefficient of y in the second column and coefficient of Z in the third column so we'll get developed off this tournament as negative one. No vehicle cleared the value off a D. X so it will be equals to a determined value off one to any faith. 1 43 139 111 101 Averaging these religious value in the first column coefficient of y in the second column and coefficient of Z in the third column. So you get the really of this tournament. The ex US negative 107 now will conclude the value of a de vie. It will be cools to the detriment of value. Off 110 1 75 1 43 129 101 average in the coefficient of X In the first column religious value in the second column and coefficient off a Z in the third column so we'll get the really off D Y US negative. 36. The last dessert is left so desired. DZ will be quilts to the tournament. Value off 110 111 1 75 1 43 139 average in the condition of X In the first column coefficient of y in the second column on this averages value Notre color so we'll get the really off DZ as 30 toe negative with negative sane. So finally begin say that the value of X comes out to be as the extra already So one or seven. Similarly, why is it cool? Street artist six on Z is equal started to, so we can conclude that the weight off Hassan Sandro is 107. Bounce on the radar mini is Tartus expound on the weight off. McGee is 32 bones.


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