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For his summar job Juob lL organic melons the Farmer" $ Market: To allruct customers Teceunald #rld bal:ntce that has no numeric markings Jcub Jcvist clever sy...

Question

For his summar job Juob lL organic melons the Farmer" $ Market: To allruct customers Teceunald #rld bal:ntce that has no numeric markings Jcub Jcvist clever system that allon s hittt hulnce Jy Ikclon from noum| [o 40Dound; (integers only) by using exactly four individual #eiphts thut ar also inleger values.For example. if Kim #ants to buy & Honeydew melon_ Jacob might put the melon on the left side of the bulance: He would then put one counterbalance weight on the right side. If the rig

For his summar job Juob lL organic melons the Farmer" $ Market: To allruct customers Teceunald #rld bal:ntce that has no numeric markings Jcub Jcvist clever system that allon s hittt hulnce Jy Ikclon from noum| [o 40Dound; (integers only) by using exactly four individual #eiphts thut ar also inleger values. For example. if Kim #ants to buy & Honeydew melon_ Jacob might put the melon on the left side of the bulance: He would then put one counterbalance weight on the right side. If the right side is heavy he would then put his lightest wcight = the left side plunce What are the four weights that Jacob uses that allow him to balance any integer melon weights from pound through 40 pounds? If you extend this paltem, what range of melons Cal * UL weigh with counlerbalance weights?



Answers

A grocery store sells two types of carrots, organic and non-organic. Past sales records indicate that the store must stock at least three times as many pounds of organic carrots as non-organic carrots. The store needs to have at least 5 pounds of non-organic carrots in stock. The maximum inventory of carrots the store can carry is 30 pounds. (a) Use $x$ to denote the number of pounds of organic carrots in stock. Use $y$ to denote the number of pounds of non-organic carrots in stock. Write a system of linear inequalitics that describes the possible numbers of pounds of each type of carrot the store could keep in stock. (b) Graph the region that represents all possible amounts of organic and non-organic carrots the store could have in stock.

Hair. In this problem, there are two parts that we have to solve. So festival always holding the A part on. In the a part, we have to write the system off leaner inequality for the given condition. On the condition is that grocery store have two types of carrot. First, organic on the next one is a non organic. No, it is given that we must have stock at least three times as many pounds off organic carrots as known or unique. It's that means X should be greater than or equals 23 way where X denotes the number of pounds of organic carriage on. Why denotes the number off pounds off non Korean Garrett now? The next statement given is that the store and needs to have least £5 off a non organic get it. That means 40 saying is, why should be greater than or equals 25? Now the maximum Garrett in the inventory should be £30. That means explains, why is less than or equals 2 30 Now these other leaner, integrated digit were able to obtain from the given statement. Now I'll be graphing these Lena inequality on a graph paper to represent all the possible amount of organic and non organic carrots at the store. So that's still there are fever now. So this is the Y axis on. This is the X axis. No, this line represents the equation. X is equals to three way on. This line represents the equation explains. Why is it cools too touchy on this one represents Why is equal to five now? The common region for the up change inequality would be this region. So this is a region that represents all the possible amount of organic and non organic character carrots the store could having stock.

Using the information provided. Let's answer the questions I followed for a, how many pennies do you have? So we have a total of 636.3 g of pennies. Yeah. And we're told that Each penny weighs an average of 3.03 g per one penny. Yeah. Therefore, yeah, we would have, We'll do this to three sig figs 1.93. 3 Times 10 to the three g of um would be the weight of our pennies for b. How many times would you need to purchase as much candy as possible? So here we have uh 0.23 so two dimes. If we just use our dimes um 1, 23 times 10 is equal to $2.30 And $2.30 times one dime equipment. Put 10. So we would need 23 dimes to purchase as much candy as possible, perceive How much longer your dimes way. So if we have 23 dimes one time As an average weight of 2.29 grounds. So we would wait 53 g for our dimes for d how many pieces of candy could you buy based on the number of dimes from part B. So from part B. We know that um We're going to have $2,30 worth of dimes and .2344 pieces of candy. And this would yield 40 pieces of candy. Great. Ive. How much would this candy way? So we know we have 40 pieces of candy. Yeah. one piece of candy weighs 10.23 grounds. Therefore this would be equal to, We want to make this one. Sigfig 400 g. And uh yeah. How many pieces of candy could you buy with? Twice as many times. So twice as many times we would have 46 times times .23 and four pieces. And the So we will be able to buy 80 pieces of candy. We had

In this example, we are working with the labor market for an individual firm and the market as a whole for the pencil market, we're assuming that these both of these markets are perfectly competitive and we're given that the market wage is $150 per day. Part A here is asking us to identify what the profit maximizing amount of labor rule would be. And we know that that's where price is equal to marginal revenue. And then part B is asking us to identify or to calculate what the price of a box of pencils is if the marginal product of the last worker hired is 30 boxes of pencils. So let's go ahead. Let's jump back to part A here to this profit maximizing rule and recognize the fact that our marginal revenue right here is really equal to our marginal product times are price And that's going to be equal to our wage, which was 150 as given to us. So we're now going to use this piece of information that marginal product times price is equal to 150 to calculate the price of the box of pencils. So Assuming as was given to us that this marginal product is equal to 30. I'm gonna multiply that by p. Because we're trying to find price and setting that equal to 150. Then all we need to do is solve for p. to get with that price of box of pencils is that tells us that the price of box of pencils is equal to $5. We did that by taking 150 divided by 30. Alright now part C. And D. Right here. But we want to do is first start by sketching out the supply and demand curves within the pencil market as a whole and within this individual firms market. So we know that we're always for this um pencil market we have uh upward sloping supply curve and we have a downward sloping demand curve. And then for this firm market, what we have is still a nice downward sloping demand curve that hasn't changed, but our supply curve here is instead horizontal. And what we were told initially is that our wage in this market is 150, so we can put that information in and that's going to be the same in the firm. They're going to be forced to accept that labour that that market wage because it's perfectly competitive, they they're not going to go any higher or lower than that, they're just going to take what wage the market is giving them. But now what we want to do for part D. Here is we're assuming that some of these workers within the pencil market have decided to switch to the computer industry, so as a result of them switching to the computer industry. In this overall pencil market, we're going to see our supply of labor decrease or supply curve is going to shift to the left from S. Note to S. One. And as a result we also see our wage increase. So are wages going to go from 150 up to some new wage. But we know that that is higher than what it was now as a result of the wage increasing within the pencil market. Going back to the fact that both of these markets are perfectly competitive. That means that this individual firm is going to have to accept that new wage. So we see the supply curve maybe shift upward, But we see that price change, so our new price has gone from 150 up to that same W. one. So we're seeing an increase in the wages as a result right here. Now this increase in a number of workers would typically decrease marginal product of labour and it works the other way as well. So because we're seeing this reduction of supply as we saw in this pencil market over here, our supply reduced from S. No. Two S. One we're going to see is the marginal product of labour at this individual firm is going to increase because they now have fewer workers. So overall, even though what we saw in the firm market that supply curve looks like it shifted upwards really, it was just showing that our wages were increasing but they have fewer workers. Right? You see this flanker went up, however, we were sitting over here at Q. Zero and now we're at Q. Once or quantity of labour has gone down. So because the quantity goes down, we see this marginal product of labour increase because there's fewer workers now

Okay for this problem, we are asked to set up a system of inequalities and then graphic based on this word problem. And so we're dealing with two types of fertilizer A and B. So fertilizer A is gonna be our X variable fertilizer B is gonna are y variable. And then we've got three different things we're dealing with. We're dealing with, um, phosphoric acid, nitrogen and potash. We're going with the pounds of those. And so first, let's focus on the phosphoric acid. So for a there are £20 that's 20 times a, which is X and then for B, there are 10 so that's plus £10 for fertilizer B. And it's said that these have minimum requirements. So when you have minimum requirements, you have to be greater than or equal to, and the minimum for this is for 60. Then we move on to, um, nitrogen and nitrogen has £30 required for a and 34 B, and the minimum requirement for this one is 960 and the last one is potash. And for a it's £5 for be it is £10 the Mac the minimum has to be to 20 and then your X and Y have to be greater than or equal to zero because you can't have negative pounds of something. Um and that's it. So sorry. Not pounds. It would be cubic yards. X and y represent cubic yards of the mix. So there's your system of inequalities. We're now gonna take that system, and I'm gonna show you on a screenshot from Dez. Most this is I put in the three equations I didn't put the X and the Y greater than zero equals here because that's just the X and y axis. And both of these, even though I only read the road equations, here's that you wouldn't get the confusing shading in here, these airboat all greater than or equal. And so the shading is gonna be above those lines. Um, so if I'm gonna go above the lines, then that's gonna be everything up here above the red there it's gonna be everything above this blue line down here and then above the green line down here and then everything in this space up here. So this is an unbounded region, but you can just get more and more and more. And so obviously the production. Hey, they can produce, um, they can get more fertilizer. They're allowed to. There's no maximum there. And so the corner points 0 46 That means that you would get none of a and 46 cubic yards of B or over here you have 44 zeroes. That's 44 cubic yards of a and zero of B, and then you've got these two corner points that work 14 of 18 of being 20 of eight and 12. So that represents all the feasible solutions, and again, it's a unbounded region.


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