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Construetion A building contractor has agreed to build six ranch-style houses, seven Cape Cod-style houses, and 14 colonial-style houses. The number of units of raw materials that go into each type of house are shown in the matrix
$$
\begin{array}{c}{\text { Steel Wood Glass Paint Labor }} \\ {\text { Ranch }\left[\begin{array}{ccccc}{5} & {22} & {14} & {7} & {17} \\ {7} & {20} & {10} & {9} & {21} \\ {6} & {27} & {8} & {5} & {13}\end{array}\right]}\end{array}
$$
Assume that steel costs $\$ 1600$ a unit, wood $\$ 900$ a unit, glass $\$ 500$ a unit, paint $\$ 100$ a unit, and labor $\$ 1000$ a unit.
(a) Write a $1 \times 3$ matrix $B$ that represents the number of each type of house to be built.
(b) Write a matrix product that gives the number of units of each raw material needed to build the houses.
(e) Write a $5 \times 1$ matrix $C$ that represents the per unit cost of each type of raw material.
(d) Write a matrix product that gives the cost of each house.
(e) Write a matrix product that gives the product $B R C .$ What does this matrix represent?

Welcome back. Okay, so we're in Section 3. 30.6 of the man is pre Calculus 2010 edition against the eighth edition, Page 3 12, number 56. Okay. All right, so in this question, or ask to redo question 53. But I think that's a typo. Because 56 says we're making 884 dollar per month payments on $86,000 mortgage. But in 53 they have a 30 year mortgage at 8.275%. I think e think they're actually redoing question 55 which has payments of 50. Okay, so all right, so I'm gonna take the interest rate, which is 12 8% a p r from question 55 instead. Okay. All right. Just to that. So here's the situation. Um, you could be making payments of $884. 61 cents for an $86,000 mortgage for 10 years. Okay, so let's take a look at the present value. So present value is equal to the payment per term in this case per month of one minus, uh, quantity one minus three rate per term in this case per month to the negative and the number of terms and a number of payments over that same interest rate. Right. So let's see how much we paid. If we're paying 884th dollars and 61 cents. Okay, you got one minus. Um, sorry. This is a plus one. Plus. Now it's 12% of 120.12, and there's 12 payments being done monthly. All right, so over 12 and the same thing with point 12/12 point of one to the negative end this part. So this is one point of one to the negative end, which is negatively 12 payments for 12 payments for year for 10 years, 120 payments. There you go. So this tells me how much I will have paid by then. Right? All right, so this is $884. 61 cents times one minus 1.1 to the negative. 1 20 all over one. That All right, So that's what I'm gonna calculate. Okay, here we go. Okay. So let's get a calculator. Okay. That's calculator. Was my calculator. There it is already. So let's see. So it's $884.61 times Let's see out for y equals rational one minus 1.1 to the negative 1. 20 over 0.1. And that that's close. The quantity. And that means well paid. 61,000 $61,607.78. Okay, so let's write that down. So that is approximately to the nearest sent, 61,000 $657.78. Okay, so what does that mean? Well, we were trying to pay off in $86,000 mortgage. So what's 86,000? Minus 61,000? This is dollars, right? For 7.78. And you know what? I just I don't feel like doing it this way. The suit on the calculator. Come on, calculator. So it's gonna be $86,000 mortgage minus that amount. Then we get $24,342. 22 cents. Okay, so let's see what that is. So it's gonna be 24,000 $342.22. Now, the thing is this, we're gonna now change your payments from $884.61 per month Did 1000 50 per month And see how many more payments? You know, we did 120 payments, you know, 12 payments per year for 10 years. Right? So the question is, how long is the term of the loan? It's gonna be less than 30 years that you originally were gonna dio, right? Um, so we're gonna use the present value formula again. Okay, here we go. So the present value now is a present value is the payment times one minus quantity one plus tau interest rate per payment to the negative end. Number of payments all over the interest rate. Right. And we're still talking about 12% per month, so 120.12% for years of one per month. Okay, so we wanna pay off 24,000 remaining, 342,000, 20 cents roughly. And my new payment is 1050 per month. And so the question is, can we solve for N? So it's one minus. I remember ours point 12/12 10.0.1. So one plus point of one is one point or one to the negative end all over point. 01 Now we want to sell for end. So let's divide by 2050. 366,022 cents, divided by 1050 Leaves one minus 1.1 to the negative end delightedly point a one. All right, let's one play both sides. We point a 1 to 100 others survived. By 100 you get $24,342. 22 cents over 105,000 is one minus 1.1 to the negative end. All right, so if we subtract this fractional from both sides and add this exponential to both sides, we get 1.1 to the negative end is one minus that crazy fraction already. Mhm. So now we take the log of both sides. We're gonna get negative. N l n take your lug of your favorite pace. Favorite base rate of 1.1 is Thea Ln of this mess, one minus two for 24,300 to 1 to 2 over 105,000. Okay. And so we divided by a negative. Ellen at 1.1. We get in and is negative. Ln of, um, Hang on. I wrote this a little bit sloppy. Yeah, this one is not part of the fraction. Right? So let's clean it up. It's one minus 24,000 over 105,000. There you go. Yeah. So it's Yellen of one minus 24,342 to 2 over over 105,000 over Ellen of 1.1. So and is approximately how many more payments? So we did 10 years. And now how many more years instead of 20 more years? Because it was also 30 year term mortgage in question 55. This basic question 55 that's the type of 53 was 55. All right, so let's put that in the calculator. So it's negative Ln off. Okay, So could waiting on. Should I write this down with my pen? Oh, get from it. Oh, boy. It's negative. Ellen of that over Ln of that. Okay. Okay, I get it. So let's get the calculator out calculator using this simulator on TV for plus c Super Edition. Here we go. All right. So it's gonna be Alfa y equals rational negative. Ln of one minus, Alfa y equals rational. Just to make it easy to read for you guys. Um 24,342 and 22 over 105,000. Close that parentheses, writing over the island of 1.1 the l n at 1.1. And that gives you 26.5 more payments. Roughly well to the nearest half a month. Alright, So 26.5. Roughly. All right. Good. Okay. Yeah, that's about 26.4 wives, 26.5. So instead of instead of another 20 years or 240 payments, it's only 26.5 payments. That's good. Okay, good. Nice. Already. So 26.5 payments initial. 26 2016 payments. Mm. So tormented. Tend to pay off is alright. So to amount of time to pay this off is the 10 years that we did already. So time equals the 10 years we did already. Plus well, 26.5. Let's see, divided by 12 goes to remainder 2.5. So it's gonna be 10 years plus two years. Let's see 2.5 months. Let's make it three months. So 3/12 is one quarter. It's about 12.25 years. There you go. Good. Now, Part B says, How much money did you save? All right. Well, let's find out. Let's go. Whoa. How much money did just say by doing that? Alright, so let's compare what we would have been paying on the calculator way would have been paying for 30 years. Um, 12 payments per year of 884,000. 61 cents. Right? That would do that, right? Yeah. So it would have been paying 318,000. Isn't an 86,000 that long? $318,459.60. Right? But now what we did, we did this. Instead, we did 120 payments for 10 years, times the 800 $84. 61 cents. Right. But then we did approximately, um 26.5 payments times 1000 50. So how much money did was pay now only 100 1,003,000. 20 cents. While that's a big savings. So question is what is the savings. Let's take what we would have paid for 30 years. Minus will be paid in that 12 and a quarter years and we get a savings of 184,000, $481.40. Okay. With cell phone enumerated. See you next time. Good luck with your homework. Bye bye.

Okay, so he would be a little bit more of genetics. Um, and particularly looking at these horses and trying to sort out what might be their genome types from their mating patterns or the offspring patterns. So we have, um, three types of horses here. We have a chestnut horse, which is a nice brown. The crime, mellow kind of sounds like marshmallow. That one is white. And then the palomino right, which is 10. Okay. And I think if you read them in the order that listed in the table, it becomes a little bit harder to parse out. But if we start with the very final part of the table, which was chestnut slash deep brown horse crossed with crim L O, which is also our white horse. We ended up with 100% tan horses slashed the palomino. Well, this looks like a lot of our crosses. We did in with the pundits squares right where we start with, um, a Hamas I Ghous of one tree and Hamas areas of another tree, and then cross it to get 100% offspring of one kind on DSO. That seems to be happening here. Okay, so I would argue Thean inheritance is one where the two wheels are coming from these chestnut brown horse and the cream ello white horse, but that since they make a tan horses probably a co dominance for you. It said it's not CO dominance. Us getting ahead of myself is incomplete. Dominant. Right? So that's when um, the colors blend. Okay, so that's part B part A is what kind of inheritance is happening here. Um and so party used to assign some symbols so you can choose any symbols you want. I am simply going to go with a capital B for chestnut. A lower case B for Carmelo. Actually, it be, uh, you know, Hamas, I guess with capital B for chestnut homeless, I guess for lower case B for Carmelo, that would mean when we cross those two, we get exclusively. Um when? Bigby when that'll be palomino. And you can even if we do this with the rest of the table, right? We see. For example, when we cross chestnut with chestnut, we ended up with 100%. Uh huh. Okay, Chestnut. Same with when we did the Carmelo cross, we cross to Carmelo's and we get a 100% crim l o offspring, population. Now, when we cross the two palominos, this is the standard cross right where we would get 25% of the head. Rosie is. And then 50% headers, I guess. And we saw in the table where we got, um, 13 of the palominos and then six and five each of the chestnut and Carmelo. And so that's roughly on par with what we'd expect there as well. So you can you can tell the rest of the table that way if you are so inclined. But the point of this it was really just thio. See that we can break down these traits into these Leal's that were very familiar with working already.

So if we start by simplifying the second line of the equation of the Peace Prize function, we'll get this 40 classes. You're 130 T minus 0.3 times 200 which is 60. So this is your seat with a negative 20. Plus, it is your 0.30 t not to start graph e using point plotting. We know that from 0 to 230 hour. Why is 40 We have a horizontal line here until we have Wise Eagle. Or until we have Texas, You got 200. So this point here is 200 comma 40. And then after that, we can plug in to 50 into negative 20 plus 0.3 t What will get us 55? So we have a point here, but 2 50 com a 55 No free plug. Innings 300. What will get us 70? Who? You have 70 about here. And we can't just assume that this keeps going up and up and up and that this is paragraph and everything like this point as well as 300 coma, 70

So if we were to simplify the algebraic expression in the second line piece wise function, we would have 30 plus 0.3 zero t minus 1 20 comes here 200.3 because equal to 36. So this is you with a negative six plus 0.3 zero t. Now we really use point plotting to graft the function up until t equals 1 20 How were wildly, people? 30. So that it would be good is to about here to be several horizontal line until 1 20 here. And then once we got to 1 20 if we would upon a 1 40 into negative sex called 0.3 times 1 40 that would be cool. 36. So who would have 36 one for you come with 36 about here. And if we were playing in 160 into that equation, we get this 42. So that gets us to about here till this line just keeps going straight up in this trajectory. In this point, let's mark it up. Has 1 20 coma 30. This point here is 1 40 Call a 36 and then 16 he come off for you too.