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The weekly revenue from the sale of x units of _ senvice given by 2-) 4x - 7z2 thousand dollars, where 0 <*< How many units should be sold maxlmlze the revenu...

Question

The weekly revenue from the sale of x units of _ senvice given by 2-) 4x - 7z2 thousand dollars, where 0 <*< How many units should be sold maxlmlze the revenue?AnsverTablesKeypad Keyboard Shortcutsunits

The weekly revenue from the sale of x units of _ senvice given by 2-) 4x - 7z2 thousand dollars, where 0 <*< How many units should be sold maxlmlze the revenue? Ansver Tables Keypad Keyboard Shortcuts units



Answers

If a manufacturer sells $x$ units of a certain product, revenue $R$ and cost $C$ (in dollars) are given by $$\begin{array}{l} R=20 x \\ C=2000+8 x+0.0025 x^{2} \end{array}$$ Use the fact that profit = revenue - cost to determine how many units the manufacturer should sell to enjoy a profit of at least $\$ 2400$.

All right. So we know the revenue function is X times 50 minus point 0002 X and the cost function will be toe vics plus 150 thought. So the question the first question is, too, to determine how many how many genes must be so in order to obtain this prophet. All right, so we know that the prophet is the revenue minus two cost, and we want to obtain an list, this prophet. All right, so we just plucked the value. We just plugged the function actually here, too. All right, So if we expand this and you put the right hand side to the Levins and you must manipulate with there's inequality and finally you will get right. So we must be familiar with this, right? That the answer will be an interval in between this to value. All right, So the interpretation of this is as long as you saw that the units in between this to value, you're gonna attend the the profit that is quitter than this value s so that their court there, Courtney accordingly, the pressure prison, it will be price per unit. Be the revenue over what the normal B divided by the larger number and the opera bellaby divide about this small number. Well, this to revenue will be different because our wall will be the revenue in terms of this Selves. And that'll be this cells. If you pluck in you find the nor bomb being 30 press per unit in the are profound being 32. All right, So our warm is when you plug this value to the revenue equation are too. It is when you plug this value, did the revenue function

Here. Total revenue from the sale of 100 tablets will be given by the formula. Artifacts is a cool sto 200 100 g x minus off 0.4 in tow. Backs scare. Now substituting X is equal 200. So we will have that I know at 100 tablets physicals to 280 in 200 minus off 0.400 whole skill. So this will be a cools to 28,000 minus off 4000 and this will be close to 24,000 dollars.

Problem. Oh, what units here say we want in the problems that are okay, you are able to see now we need to replace RNC with their Russians in terms of X. Also again, that's the given information. So ours you go. The 3.29 times X and cost is equal to smiley. Face. Cost is equal to 2.4 Closed 5000 600. And let's fix that for that's a little bit funky, huh? Guess we're just gonna leave it. Never mind. So hopefully you can read. That's 2.0 for axe. And just erase that little doctor. All right, So what's the first step in solving this equation? Will we see? We need to find We need a software exit. We have toe isolate X. The first step, I would say it would be to move this 2.42 left side by subtracting it. And hopefully you can recall that it does not like force what we do to one side of the equation. We must do to both sides. Otherwise we change the value. The equation. Here we go. This is writing a little better now. All right? So after we do this attraction were left with 3.29 x minus 2.4 x on the left side, which is one 0.25 times X. And on the right side, we see that the 2.4 minus 2.4 ex, um, those two terms cancel. Right? So we're left with just 5000 times 5600. So 5600 is he got a 1.25 X. So we just need to divide by that one and 1/4 in order to isolate X because we want extra have just the coefficient of ones that were divided by 1.25 on both sides. I'm showing the steps in red here, but what I'm doing in between all right, And after we divide, we're left with just acts on the left side. No one time sex there on the left side and on the right, we have the final answer 4000 400 and 80 units. So don't forget your you. It's are simply all right. So this is our final answer again to interpret this within the context of the problem What did we just find? Well, we found the number of units we needed to sell in order for C two. Equal are. And if you want to check yourself, you can take this value substituted back into the original expression for sea and for our for the X value. Here, you'll find out that those to come out to be equivalent. All right, Thank you.

So they give us the formula. This problem that revenue is equal to negative. Three X squared plus 600 x uh, plus 1000. And without having done the calculus yet, all that we know is that this graph is going to look something like this goes up and then comes back down. So the maximum value is going to be the Vertex. Well, we find the Vertex by doing the formula negative B over two A. So, as you look at this, you can say Okay, well, the B value 600. So it's negative 600 over two times the a value of negative three. So looking at negative 600 divided by 2000 and three is negative. Six. So he gets 600 whatever the units are, uh, sorry. 600 divided by six is 100. Um, I guess items or computers, uh, you know, whatever. Whatever the units are, I circled in green. So then in part B, when it's asking, what is the maximum? Probably knew. Well, now you just have to plug in 100 and for X. Now we go to a calculator. Not that I couldn't do this in my head, but uh huh, I guess I could and replace the excess was 100. So just make sure you do this correctly. You know that one times one times three is negative. Three on 234 zeros six times, one with four zeros, Another one of those. So I was at 30,000. So we're looking at $31,000 and feel free to use a calculator to verify that answer. But this is what we want. That's your answer to A and here's your answer for B chief.


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