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Jennifer owns her own toy company and is getting ready for Black Friday: She uses a separate shipping company to ship the items and a separate payment company to re...

Question

Jennifer owns her own toy company and is getting ready for Black Friday: She uses a separate shipping company to ship the items and a separate payment company to receive payment from the customers. Each toy is S16.25 each: The cost is S4.50 to make each toy: Shipping is S0.30 per toy: The payment company charges Jennifer 2% on the cost of each toy sold Jennifer pays S5.00 a month for her company'$ website.Part A) Introduce a variable for the number of toys that Jennifer sells. Create a line

Jennifer owns her own toy company and is getting ready for Black Friday: She uses a separate shipping company to ship the items and a separate payment company to receive payment from the customers. Each toy is S16.25 each: The cost is S4.50 to make each toy: Shipping is S0.30 per toy: The payment company charges Jennifer 2% on the cost of each toy sold Jennifer pays S5.00 a month for her company'$ website. Part A) Introduce a variable for the number of toys that Jennifer sells. Create a linear expression for the amount of money Jennifer makes monthly depending on how many toys she sells. Simplify the expression completely:



Answers

An artist makes jewelry from polished stones. The rent for her studio, Internet service, and phone come to $\$ 640$ per month. She also estimates that it costs $\$ 3.50$ in supplies to make one necklace. At art shows and online, she sells the necklaces for $\$ 25$ each. a. Write a linear cost function that represents the $\operatorname{cost} C(x)$ to produce $x$ necklaces during a one-month period. b. Write a linear revenue function to represent the revenue $R(x)$ for selling $x$ necklaces. c. Evaluate $(R-C)(x)$ and interpret its meaning in the context of this problem. d. Determine the profit if the artist sells 212 necklaces during a one-month period.

Yes to this question. Cursed them are similar to the last one. For a we have to write, um, a polynomial that trapped the revenue that he brings in from his paintings. Small, medium and large. They're free to the small ones he break makes 50. He starts for $50 area 50 ass. You try to make it look more like a night Berio, that DS and then for medium he makes himself the medium for 75 75 times the medium And then he still the large for 100 to 100 times the large. And that's there. A polynomial per what he charges for how much he makes in a day right now for the costs for part B. We have to subtract that because that has to go into it. That would cost him $22 1st small 3 to 22 huh? It also costs come 33 firm medium 3 33 medium. And then it'll cost him 47 for a large and that are polynomial for cost, not for the polynomial for that hit net income. After we take in to consideration of costs, we just subtract so 50 minus 22 gives it 28. So he ends up netting $28 per small. Her This one, we end up getting 42. So he next $42 per medium and then plus 53 l he next $53 per large that he so and then start. Probably no meal overall for what He net. Okay, so we come over here now and we're told we're told the numbers for what he makes in a month. So in a month, we have 28 times the number of small he sells, which he would we're told. Ah, four. Are you mixed? 42 per medium. And we're told that he's so six medium. And then we make two large the 53 time for the two large yourselves and what we get when we get that we get 28 times for which is 112 you make you $112 off this small 42 tom sticks, we get 252 three months, 252 off the medium's. And then he makes 100 60 up the large we have add all that up. And when we do that. We get 470. So in that month after the cough or considered he still next $470 per month are in this one month with the cost monitor the revenue.

And this problem. Natalia is selling magazines, so she gets a dollar 75 for every magazine that she sells. And she gets a dollar 50 for every newspaper subscriptions she sells, and her goal is to make $525 commission. So we're gonna write an equation that models for the different numbers of the magazine newspaper should or should not be sold to meet the goal. So if she did 1.7 time times their number magazine subscriptions she sells plus 1.5 times the number of newspapers prescription subscription she fells that equals 2 525 her goal. So we can change the number of M and newspapers and magazines seriously, she sells to reach 525.

FX is equal to 1 16 time X x number of months and, uh, G acts that's equal to with the axe less on late. Well, the sea and bags equals G X. 0 60 acts. What do 50 acts plus late? That is Dnx, except was like terms and they x equal do. Then damn month the planet will be seen.

So for this problem, we are given a few matrices that are going to represent the melons, squash and tomatoes sold by farmers, three Children or each day on Saturday and Sunday. I'm then friendly. Our metric see is going to give us the price per pound for each type of produce that the kids can sell. I'm so for part of this problem, we want to calculate the Matrix or the product matrix A. C. Um, so essentially, we're going to start with our first row of a in our first or only Cole with sea, and we will try these together. So when we do that to computer inner product, we first get 120 times 1200.1, which is going to be 12. We add this to 50 times 500.5, which will be plus 25. And then finally, we will add this to 60 times one so plus 60 on the next. For our second rope of A, we have 40 times 400.1, which is going to be four plus 25 times 250.5, which will be 12.5 and finally plus 30 times one will be plus 30 and Then for our third row of A. We start with 60 times 600.1, which will give us six plus 30 times point fi, which is 15 and finally plus 20 times one I'm So when we finish adding up all of these together, our first road is going to be 12 plus 25 plus 60 which we know is 97. Our second rope will be four plus 12 play five a plus 30 um, And so once we finish adding these up, we're going to get 46.50 And in our third row, we have six plus 15 plus 20 which will give us 41. So now we have our product matrix A C. And essentially, because we know that we calculated this by multiplying the Saturday profits, which was given by Matrix A by our price per pound of each fruit. I'm an added these together. He's a matrix. A C is going to give us in our first rope Amy's product on Saturday. We're total total revenue on Saturday, Um, and then our second row will be breaths. Total profit on Saturday and our third row will be Chad's total profit on Saturday. Next report. Beat. We want to you calculate the product matrix B. C. I'm so again this is essentially the same thing. We're going to go ahead and start with our first row of beat and multiply that by our only call, Missy. So we get 100 times 1000.1, which is 10 plus 60 times 600.5, which is 30 plus 30 times one. Oh, and this is going to end up being equal to 70. Next for our second row of B, we're going to multiply 35 by 350.1 plus 20 times 0.5 is 10 plus 20 which is going to give us 33 25 0 And finally, our third row B is going to be a 60 times 600.1, which is six plus 25 times 250.5, which is 12 50 and finally plus 30 times one. I'm so this is going to end up being equal to 48.50 And just like in part a, um, this time we are using our A Sunday profit matrix or products sold matrix, um, and again well flying by her price per pound of each of our vegetables that we're selling with fruits or vegetables. And so essentially, this is going to tell us of the same thing as part A Except for they're going to be our total profits made for child on Sunday. And then I'll go ahead and make a new page here to save some space to work on Port Sea of this problem s o for a party of this problem. We know we want to you calculate a matrix a plus matrix B. So essentially, we're just going to add each of our corresponding entries. I'm so, for instance, our first row and first column has 120 plus 100 which is going to give us 220. All right, a second row and first column is going to be 40 plus 35 which is 75. And then finally, we have 60 plus 60 which is 120. I'm in the next inner second call. We have 50 plus 60 which will be 110 25 plus 20 which is going to give us 45 and 30 plus 25 which will be 55 and then Finally, in our third column, we have 60 close 30 which is 90 30 plus 20 which is 50 and 20 plus 30 which is again 50. I'm so since we know that matrices A and P, we're used to represent the pounds of each product sold by each sibling on Saturday and Sunday. By adding these together, we're finding the total number of pounds of each product sold on Saturday and Sunday combined. Um, so essentially, it's just if we were to take the product sold for the entire weekend rather than for each individual day and then friendly for a party of our problem, we want to calculate a pulse beat, which is the matrix that we just calculated in part C and multiply this by Matrix C. And so we're going to be using this matrix right here and multiplying it by matrix seat. So, just as we did in part of the problem, I'm for our first row of a or of April speed. We have 220 times 2200.1, which is 22. We're adding this to 110 plus 1100.5, which is just 55. And finally Adamis to 90 times one, which is going to give us a total of 167. For our second row of A plus B. We have 75.1 plus 45 times 450.5 on, then finally plus 50 times one which is going to end up being equal to a and then in our third row of a plus B way have 12 plus 55 divided by two and finally plus 50. And this is going to end up giving us 89.50 And so, just as in parts A and B of this problem, this matrix here, the product matrix of a plus beef time, see, is going to essentially just tell us the total profit of each individual child on where our first road going to correspond to Amy. Our second roll correspond to Beth and our third Rose going to correspondent Chad. Um and this is our total profit made by each child over the entire weekend. I mean, rather than each day. And that is going to you just come from the fact that we used our product or a matrix here that came from adding our total sales on Saturday and Sunday together


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