Can anyone help me maximizing profit
up vote
-3
down vote
favorite
Hi guys i have a problem that i cant solve. its asking me to compute the optimum number of units that would maximize profit; if no more than 80 units can be built; and the resulting maximum profit.
The function is as follows:
$$
C(x)= frac{x^3}{3} - frac{55x^2}{2} + 200x + 20000
$$
i have used the quadratic formula to find 2 x values (51 and 4) and if done right i got a relative maximum at x=4
F'(x)= {x^2} - {55x} + 200
F(4)=20381.33
calculus optimization
asked Nov 16 at 4:44
Francisco Armendariz
11
add a comment |
up vote
-3
down vote
favorite
Hi guys i have a problem that i cant solve. its asking me to compute the optimum number of units that would maximize profit; if no more than 80 units can be built; and the resulting maximum profit.
The function is as follows:
$$
C(x)= frac{x^3}{3} - frac{55x^2}{2} + 200x + 20000
$$
i have used the quadratic formula to find 2 x values (51 and 4) and if done right i got a relative maximum at x=4
F'(x)= {x^2} - {55x} + 200
F(4)=20381.33
calculus optimization
asked Nov 16 at 4:44
Francisco Armendariz
11
1
what have you tried in solving the problem? include them in the question statement if possible.
– Siong Thye Goh
Nov 16 at 4:47
my tutor recommended using principles of derivatives and so i took the first deriv. and got 2 x values:(51 and 4) plugged those in and found the concavity but i just dont know if im on the right track. i found the relative max and plugged it into the original function and got an answer but i know its not what im looking for
– Francisco Armendariz
Nov 16 at 4:50
you are encouraged to include your attempt in your original post.
– Siong Thye Goh
Nov 16 at 4:53
Sorry, im so desperate i forgot to. after computing the deriv. of the first equation, i plugged in X=4 which i assume would be the number of units that maximizes profit. my attempt was ((4^3)/3) - ((55(4^2)/2) + 200(4) + 20000 which gave me an answer of $20381.33 i computed a number of units and the resulting profit from it but dont know if i used the right functions or values
– Francisco Armendariz
Nov 16 at 5:08
You are receiving $3$ negative votes for not including your attempts (none by me). There is an edit button that you can click on and edit your post. here is a reference for typsetting maths on this site. I don't think $4$ or $51$ are the exact roots.
– Siong Thye Goh
Nov 16 at 5:14
add a comment |
up vote
-3
down vote
favorite
up vote
-3
down vote
favorite
Hi guys i have a problem that i cant solve. its asking me to compute the optimum number of units that would maximize profit; if no more than 80 units can be built; and the resulting maximum profit.
The function is as follows:
$$
C(x)= frac{x^3}{3} - frac{55x^2}{2} + 200x + 20000
$$
i have used the quadratic formula to find 2 x values (51 and 4) and if done right i got a relative maximum at x=4
F'(x)= {x^2} - {55x} + 200
F(4)=20381.33
calculus optimization
asked Nov 16 at 4:44
Francisco Armendariz
11
Hi guys i have a problem that i cant solve. its asking me to compute the optimum number of units that would maximize profit; if no more than 80 units can be built; and the resulting maximum profit.
The function is as follows:
$$
C(x)= frac{x^3}{3} - frac{55x^2}{2} + 200x + 20000
$$
i have used the quadratic formula to find 2 x values (51 and 4) and if done right i got a relative maximum at x=4
F'(x)= {x^2} - {55x} + 200
F(4)=20381.33
calculus optimization
calculus optimization
asked Nov 16 at 4:44
Francisco Armendariz
11
asked Nov 16 at 4:44
Francisco Armendariz
11
edited Nov 16 at 5:26
asked Nov 16 at 4:44
Francisco Armendariz
11
asked Nov 16 at 4:44
Francisco Armendariz
11
asked Nov 16 at 4:44
Francisco Armendariz
11
11
1
what have you tried in solving the problem? include them in the question statement if possible.
– Siong Thye Goh
Nov 16 at 4:47
my tutor recommended using principles of derivatives and so i took the first deriv. and got 2 x values:(51 and 4) plugged those in and found the concavity but i just dont know if im on the right track. i found the relative max and plugged it into the original function and got an answer but i know its not what im looking for
– Francisco Armendariz
Nov 16 at 4:50
you are encouraged to include your attempt in your original post.
– Siong Thye Goh
Nov 16 at 4:53
Sorry, im so desperate i forgot to. after computing the deriv. of the first equation, i plugged in X=4 which i assume would be the number of units that maximizes profit. my attempt was ((4^3)/3) - ((55(4^2)/2) + 200(4) + 20000 which gave me an answer of $20381.33 i computed a number of units and the resulting profit from it but dont know if i used the right functions or values
– Francisco Armendariz
Nov 16 at 5:08
You are receiving $3$ negative votes for not including your attempts (none by me). There is an edit button that you can click on and edit your post. here is a reference for typsetting maths on this site. I don't think $4$ or $51$ are the exact roots.
– Siong Thye Goh
Nov 16 at 5:14
add a comment |
1
what have you tried in solving the problem? include them in the question statement if possible.
– Siong Thye Goh
Nov 16 at 4:47
my tutor recommended using principles of derivatives and so i took the first deriv. and got 2 x values:(51 and 4) plugged those in and found the concavity but i just dont know if im on the right track. i found the relative max and plugged it into the original function and got an answer but i know its not what im looking for
– Francisco Armendariz
Nov 16 at 4:50
you are encouraged to include your attempt in your original post.
– Siong Thye Goh
Nov 16 at 4:53
Sorry, im so desperate i forgot to. after computing the deriv. of the first equation, i plugged in X=4 which i assume would be the number of units that maximizes profit. my attempt was ((4^3)/3) - ((55(4^2)/2) + 200(4) + 20000 which gave me an answer of $20381.33 i computed a number of units and the resulting profit from it but dont know if i used the right functions or values
– Francisco Armendariz
Nov 16 at 5:08
You are receiving $3$ negative votes for not including your attempts (none by me). There is an edit button that you can click on and edit your post. here is a reference for typsetting maths on this site. I don't think $4$ or $51$ are the exact roots.
– Siong Thye Goh
Nov 16 at 5:14
1
1
what have you tried in solving the problem? include them in the question statement if possible.
– Siong Thye Goh
Nov 16 at 4:47
what have you tried in solving the problem? include them in the question statement if possible.
– Siong Thye Goh
Nov 16 at 4:47
my tutor recommended using principles of derivatives and so i took the first deriv. and got 2 x values:(51 and 4) plugged those in and found the concavity but i just dont know if im on the right track. i found the relative max and plugged it into the original function and got an answer but i know its not what im looking for
– Francisco Armendariz
Nov 16 at 4:50
my tutor recommended using principles of derivatives and so i took the first deriv. and got 2 x values:(51 and 4) plugged those in and found the concavity but i just dont know if im on the right track. i found the relative max and plugged it into the original function and got an answer but i know its not what im looking for
– Francisco Armendariz
Nov 16 at 4:50
you are encouraged to include your attempt in your original post.
– Siong Thye Goh
Nov 16 at 4:53
you are encouraged to include your attempt in your original post.
– Siong Thye Goh
Nov 16 at 4:53
Sorry, im so desperate i forgot to. after computing the deriv. of the first equation, i plugged in X=4 which i assume would be the number of units that maximizes profit. my attempt was ((4^3)/3) - ((55(4^2)/2) + 200(4) + 20000 which gave me an answer of $20381.33 i computed a number of units and the resulting profit from it but dont know if i used the right functions or values
– Francisco Armendariz
Nov 16 at 5:08
Sorry, im so desperate i forgot to. after computing the deriv. of the first equation, i plugged in X=4 which i assume would be the number of units that maximizes profit. my attempt was ((4^3)/3) - ((55(4^2)/2) + 200(4) + 20000 which gave me an answer of $20381.33 i computed a number of units and the resulting profit from it but dont know if i used the right functions or values
– Francisco Armendariz
Nov 16 at 5:08
You are receiving $3$ negative votes for not including your attempts (none by me). There is an edit button that you can click on and edit your post. here is a reference for typsetting maths on this site. I don't think $4$ or $51$ are the exact roots.
– Siong Thye Goh
Nov 16 at 5:14
You are receiving $3$ negative votes for not including your attempts (none by me). There is an edit button that you can click on and edit your post. here is a reference for typsetting maths on this site. I don't think $4$ or $51$ are the exact roots.
– Siong Thye Goh
Nov 16 at 5:14
add a comment |
2 Answers
2
active
oldest
votes
up vote
0
down vote
Guide:
$$C'(x) = x^2-55x+200$$
Use quadratic formula to solve for the root. Evaluate the $C$ value at those locations.
Also, evaluate $C$ at $x=0$ and $x=80$. Big hint: This step is very important.
Here is a related picture where I have plotted $frac{C}{10^3}.$
answered Nov 16 at 5:06
Siong Thye Goh
93.8k1462114
add a comment |
up vote
0
down vote
Calculus could be used to solve for this. First derivative will tell us the maximum/maximize value.
So:
d/dx yeilds:
x^2 - 55x +200 =0
So now use Quadratic equation you get
(55 +/- sqrt(89))/2
So either 3.91 (4) or 51.08 or 51. Hence 4 is the correct answer. You can verify this by plugging values back into C(X) and see which is higher.
answered Nov 16 at 6:06
CooperH
12
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Guide:
$$C'(x) = x^2-55x+200$$
Use quadratic formula to solve for the root. Evaluate the $C$ value at those locations.
Also, evaluate $C$ at $x=0$ and $x=80$. Big hint: This step is very important.
Here is a related picture where I have plotted $frac{C}{10^3}.$
answered Nov 16 at 5:06
Siong Thye Goh
93.8k1462114
add a comment |
up vote
0
down vote
Guide:
$$C'(x) = x^2-55x+200$$
Use quadratic formula to solve for the root. Evaluate the $C$ value at those locations.
Also, evaluate $C$ at $x=0$ and $x=80$. Big hint: This step is very important.
Here is a related picture where I have plotted $frac{C}{10^3}.$
answered Nov 16 at 5:06
Siong Thye Goh
93.8k1462114
add a comment |
up vote
0
down vote
up vote
0
down vote
Guide:
$$C'(x) = x^2-55x+200$$
Use quadratic formula to solve for the root. Evaluate the $C$ value at those locations.
Also, evaluate $C$ at $x=0$ and $x=80$. Big hint: This step is very important.
Here is a related picture where I have plotted $frac{C}{10^3}.$
answered Nov 16 at 5:06
Siong Thye Goh
93.8k1462114
Guide:
$$C'(x) = x^2-55x+200$$
Use quadratic formula to solve for the root. Evaluate the $C$ value at those locations.
Also, evaluate $C$ at $x=0$ and $x=80$. Big hint: This step is very important.
Here is a related picture where I have plotted $frac{C}{10^3}.$
answered Nov 16 at 5:06
Siong Thye Goh
93.8k1462114
edited Nov 16 at 5:15
answered Nov 16 at 5:06
Siong Thye Goh
93.8k1462114
answered Nov 16 at 5:06
Siong Thye Goh
93.8k1462114
answered Nov 16 at 5:06
Siong Thye Goh
93.8k1462114
93.8k1462114
add a comment |
add a comment |
up vote
0
down vote
Calculus could be used to solve for this. First derivative will tell us the maximum/maximize value.
So:
d/dx yeilds:
x^2 - 55x +200 =0
So now use Quadratic equation you get
(55 +/- sqrt(89))/2
So either 3.91 (4) or 51.08 or 51. Hence 4 is the correct answer. You can verify this by plugging values back into C(X) and see which is higher.
answered Nov 16 at 6:06
CooperH
12
add a comment |
up vote
0
down vote
Calculus could be used to solve for this. First derivative will tell us the maximum/maximize value.
So:
d/dx yeilds:
x^2 - 55x +200 =0
So now use Quadratic equation you get
(55 +/- sqrt(89))/2
So either 3.91 (4) or 51.08 or 51. Hence 4 is the correct answer. You can verify this by plugging values back into C(X) and see which is higher.
answered Nov 16 at 6:06
CooperH
12
add a comment |
up vote
0
down vote
up vote
0
down vote
Calculus could be used to solve for this. First derivative will tell us the maximum/maximize value.
So:
d/dx yeilds:
x^2 - 55x +200 =0
So now use Quadratic equation you get
(55 +/- sqrt(89))/2
So either 3.91 (4) or 51.08 or 51. Hence 4 is the correct answer. You can verify this by plugging values back into C(X) and see which is higher.
answered Nov 16 at 6:06
CooperH
12
Calculus could be used to solve for this. First derivative will tell us the maximum/maximize value.
So:
d/dx yeilds:
x^2 - 55x +200 =0
So now use Quadratic equation you get
(55 +/- sqrt(89))/2
So either 3.91 (4) or 51.08 or 51. Hence 4 is the correct answer. You can verify this by plugging values back into C(X) and see which is higher.
answered Nov 16 at 6:06
CooperH
12
answered Nov 16 at 6:06
CooperH
12
answered Nov 16 at 6:06
CooperH
12
answered Nov 16 at 6:06
CooperH
12
12
add a comment |
add a comment |
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3000727%2fcan-anyone-help-me-maximizing-profit%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
what have you tried in solving the problem? include them in the question statement if possible.
– Siong Thye Goh
Nov 16 at 4:47
my tutor recommended using principles of derivatives and so i took the first deriv. and got 2 x values:(51 and 4) plugged those in and found the concavity but i just dont know if im on the right track. i found the relative max and plugged it into the original function and got an answer but i know its not what im looking for
– Francisco Armendariz
Nov 16 at 4:50
you are encouraged to include your attempt in your original post.
– Siong Thye Goh
Nov 16 at 4:53
Sorry, im so desperate i forgot to. after computing the deriv. of the first equation, i plugged in X=4 which i assume would be the number of units that maximizes profit. my attempt was ((4^3)/3) - ((55(4^2)/2) + 200(4) + 20000 which gave me an answer of $20381.33 i computed a number of units and the resulting profit from it but dont know if i used the right functions or values
– Francisco Armendariz
Nov 16 at 5:08
You are receiving $3$ negative votes for not including your attempts (none by me). There is an edit button that you can click on and edit your post. here is a reference for typsetting maths on this site. I don't think $4$ or $51$ are the exact roots.
– Siong Thye Goh
Nov 16 at 5:14