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The demand function for a product is given by5p = 8000 1 _ 5 + e-o.oo21_where p is the price per unit (in dollars) and € is the number of units sold. Find the...

Question

The demand function for a product is given by5p = 8000 1 _ 5 + e-o.oo21_where p is the price per unit (in dollars) and € is the number of units sold. Find the numbers of units sold for prices of p 8200 and p S800.

The demand function for a product is given by 5 p = 8000 1 _ 5 + e-o.oo21_ where p is the price per unit (in dollars) and € is the number of units sold. Find the numbers of units sold for prices of p 8200 and p S800.



Answers

Demand The demand function for a product is given by $p=5000\left(1-\frac{4}{4+e^{-0.002 x}}\right)$ where $p$ is the price per unit and $x$ is the number of units sold. Find the numbers of units sold for prices of $(a)$ $p=\$ 200$ and (b) $p=\$ 800$.

For the given problem We can consider this demand function. We're now it's going to be 10,000 And then we'll have 1 -3 over three plus E to the negative 0.1 X. The slight changes from the previous problem, we want to find the numbers of units sold for prices when p equals 51,500. So we could do this graphically. Another option would be for us to solve this. I was your basically. So if we put this as 500 We can then divide this by 10,000. And then what we would do is we would add one or subtract one that is multiplied by a negative ones that becomes positive, this becomes negative And then we can divide by three. We would flip the fraction subtract three and use the natural log to get our final result.

So given the price demand function, Which is key equals 14.75 Divided by one plus. Mhm. What's your .01 x. Now, I want to solve for X. In terms of P. So the way that we could do that is by multiplying this on both sides. We can also divide by 14.75. But ultimately, what we end up getting is that x equals yeah, 14 75 Over P -100. That right. There is going to be resulting function that we get. And we see that the number of units sold when the price is 10. Well, let p equal 10. We end up seeing that the number of units sold is going to be about 48 units.

Okay, We're given price in dollars of a certain commodity and the quantity X sold. Obey the following demand the equation and were also given a cost equation. The cost in dollars of producing X units is this equation the simulate, all items produced or sold. We want to find the cost. C is a function of the price P. So right now you can see that cost is a function of X. We want cost to be a function of. So we're gonna use our first equation here and we're going to solve for X. So we'll subtract 200 from both sides and then multiply both sides by negative five. So we get negative five p plus the 1000 equals X, or if we would rather 1000 minus five p is X okay, Now that we know that X is 1000 minus five p, we can go back to our cost function and substitute 1000 minus five p. Rex. Now we have cost as a function of okay,


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