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In the following exercises, solve the given maximum and minimum problems.A company finds that there is a net profit of $\$ 10$ for each of the first 1000 units produced each week. For each unit over 1000 produced, there is 2 cents less profit per unit. How many units should be produced each week to net the greatest profit?

Calculus 1 / AB

Chapter 24

Applications of the Derivative

Section 7

Applied Maximum and Minimum Problems

Derivatives

Missouri State University

Campbell University

Harvey Mudd College

University of Nottingham

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Que in the crawford of a certain song by B alls Externalizing will do 1005 100 The status It's a minus 1.5. Explore endless 1 20 violence to wise. Well, then excessive cost off a unit off liberal. And why is the cost of unit of rules? So now we have to find the values Vixen live Bridgeman wise, which maximizes profit. So first different shit be partially with respect toe. It's soapy exit mental. So this becomes you B six minus Yates said Melody. The decision should be partially with respect to why we get 1 20 minus four, right? Really? Set it off these partial elevated sequences You in order to find out the complaints 2 36 minus three eggs Zigman 20 and 1 20 minus. Why is it going to zero to realize xz Quinto 12 And why is it Will do 30. That's for the critical point are do n Kemal Deen Now we have to identified that Isn't he extreme? A two will use a test disk lament D in this case is given by being eggs eggs off. Well, come on, they're being toe be My wife wants Mary kamata D minus B x white off. Welcome on 30 square. So even flus captured it. B x x off eggs or eggs comma y that is going to be minus dream and be by my oath X come away. That is going to be minus four. That is differentiating B y partially with respect a white b x y z quinto different shading the X partial with respect Oh my God! Get Tzeitel. So all these are constants who we not have toe sub studio not a can play. Oh, be xx at that point to see who are d is going to be. Be xx off. Welcome. A 30 will be minus three and be by my oft welcome at that they will be minus fool Tu minus B X bytes anyway is going to be zero. So just well, which is greater than zero, which implies he's a creative maximum or minimum. This implies he is I do maximum more minimal. Now we will see if p x x it's created a notorious dancing pleasantly also be xx And, uh, welcome out. That day is going to be a constant, which is minus three two slash stand zero, which implies be Is it like to maximum that? Welcome out the D. So welcome authority and exit when exit will toe that does. He's maximum when exit 2012. And why is it well toe 30. So we'll substitute in the profit equation. So be off. Welcome, art. Artie is going to be 1005 100 minus 1005 100. Just look to success. And this that the 16 to 12 minus one point site. Explain lettuce Yes. Where I choose to 116 this 100 would be y what this did It is going to be 3600 minus No. Why square that this doing to the east where it is 1000 800 this 1000 Hatem Oh, a maximum often have X equal to dwells. And why is it do be? It's going to be 2516

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