Constraints 1 cup of butter and 3 cups of sugar for each...

Constraints: - 1 cup of butter and 3 cups of sugar for each batch of pancakes - 2 cups of butter and 2 cups of sugar for each batch of waffles - The chef has 8 cups of butter and 12 cups of sugar available - The profit from a batch of pancakes is $20 - The profit from a batch of waffles is $30

Transcript

00:01 Cookies and pound cakes.

00:02 So i'm going to put chocolate chip and pound cakes.

00:04 Each batch of chocolate chip cookies requires two sticks of butter, so let's put butter here, and two eggs.

00:12 Okay, and then each pound cake requires one stick of butter and four eggs.

00:19 The profit from the chocolate chip cookies is three dollars per batch, and from the pound cake is seventy seven dollars.

00:30 The bakery has 72 sticks of butter and 96 eggs.

00:36 How many should they make? the chocolate chip cookies are so popular that there's a standing order of eight batches, so that means that we need at least eight batches.

00:49 Let's go this is x and this is y, so that means x has to be greater than or equal to eight.

00:56 And how many batches of cookies and how many cakes should they make to maximize their profit? well we're going to have our equations.

01:04 They're going to have to have, they can't use any more than 72 eggs, so we're going to have no more than, i mean butter and eggs, and then this is the profit that we want to maximize.

01:15 So i'm going to go ahead and simplify this equation by dividing everything by two, so that's going to be x plus 2y equals to, or is less than or equal to 48.

01:25 So let's graph this.

01:27 So i'm going to get my graph over here.

01:29 I know x is greater than eight, so i'm already going to look at, there's eight, and i'm going to shade that here.

01:35 Now i'm going to go to the top equation, and i want to get my intercepts.

01:39 If x is zero, y is 72, and if y is zero, then x is 36.

01:45 So i'm come over here, we have 0, 72, and then we're going to have 36, 0, which is going to be out here.

01:55 And so i'm going to get that, and so i'm looking at this region.

01:59 So now i'm going to go to the next one, and i'm going to go if x is zero, y is 24, and if y is zero, we're looking at x being 48.

02:09 So that's going to be on out here, in here, so it's going to be 0, 24, and 48, 0.

02:17 So connect those, and so the region that i'm looking at is going to be here.

02:26 What are these ordered pairs? so let's get that...

Question

Constraints: - 1 cup of butter and 3 cups of sugar for each batch of pancakes - 2 cups of butter and 2 cups of sugar for each batch of waffles - The chef has 8 cups of butter and 12 cups of sugar available - The profit from a batch of pancakes is $20 - The profit from a batch of waffles is $30

Please give Ace some feedback