djdownfawl
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- Sep 28, 2010
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Please help here i figured out all the questions but this one i dont know ...........
Please help me with this question.
- Thread starter djdownfawl
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Hello, djdownfawl!
\(\displaystyle \text{They will sell 9800 bottles and make a profit of \$5 each.}\)
\(\displaystyle \text{Hence, the minimum profit is: }\:9800 \times 5 \:=\:49,000\text{ dollars.}\)
\(\displaystyle \text{Let }x\text{ = the number of additional bottles sold.}\)
\(\displaystyle \text{The profit from these bottles will be reduced by: }\:0.0003x \text{ dollars each.}\)
\(\displaystyle \text{The profit per bottle will be: }\
5 - 0.0003x)\text{ dollars each.}\) .[1]
\(\displaystyle \text{The profit from these }x\text{ additonal bottles will be: }\:x(5-0.0003x)\text{ dollars.}\)
\(\displaystyle \text{Hence, the total profit is: }\ \;=\;49,000\;+\;x(5\;-\;0.0003x) \quad\Rightarrow\quad P\;=\;49,000\;+\;5x\;-\;0.0003x^2\) .[2]
\(\displaystyle \text{And }that\text{ is the function we must maximize.}\)
\(\displaystyle \text{Set the derivative equal to zero, and solve.}\)
. . \(\displaystyle P' \;=\;5 - 0.0006x \;=\;0 \quad\Rightarrow\quad x \:=\:\frac{5}{0.0006} \;=\;\frac{25,\!000}{3}\)
Substitute x into [2]:
. . \(\displaystyle P \;=\;49,000 +5\left(\frac{25,000}{3}\right) - 0.0003\left(\frac{25,000}{3}\right)^2 \;=\;\frac{209,\!500}{3}\)
\(\displaystyle \text{Therefore, the maximum profit is about: }\:\$6,\!983.33\)
Substitute x into [1]:
. . \(\displaystyle 5 - 0.0003\left(\frac{25,\!000}{3}\right) \;=\;2.5\)
\(\displaystyle \text{Therefore, the profit per bottle will be }\$2.50\)
\(\displaystyle \text{They will sell 9800 bottles and make a profit of \$5 each.}\)
\(\displaystyle \text{Hence, the minimum profit is: }\:9800 \times 5 \:=\:49,000\text{ dollars.}\)
\(\displaystyle \text{Let }x\text{ = the number of additional bottles sold.}\)
\(\displaystyle \text{The profit from these bottles will be reduced by: }\:0.0003x \text{ dollars each.}\)
\(\displaystyle \text{The profit per bottle will be: }\
5 - 0.0003x)\text{ dollars each.}\) .[1]\(\displaystyle \text{The profit from these }x\text{ additonal bottles will be: }\:x(5-0.0003x)\text{ dollars.}\)
\(\displaystyle \text{Hence, the total profit is: }\
\;=\;49,000\;+\;x(5\;-\;0.0003x) \quad\Rightarrow\quad P\;=\;49,000\;+\;5x\;-\;0.0003x^2\) .[2]\(\displaystyle \text{And }that\text{ is the function we must maximize.}\)
\(\displaystyle \text{Set the derivative equal to zero, and solve.}\)
. . \(\displaystyle P' \;=\;5 - 0.0006x \;=\;0 \quad\Rightarrow\quad x \:=\:\frac{5}{0.0006} \;=\;\frac{25,\!000}{3}\)
Substitute x into [2]:
. . \(\displaystyle P \;=\;49,000 +5\left(\frac{25,000}{3}\right) - 0.0003\left(\frac{25,000}{3}\right)^2 \;=\;\frac{209,\!500}{3}\)
\(\displaystyle \text{Therefore, the maximum profit is about: }\:\$6,\!983.33\)
Substitute x into [1]:
. . \(\displaystyle 5 - 0.0003\left(\frac{25,\!000}{3}\right) \;=\;2.5\)
\(\displaystyle \text{Therefore, the profit per bottle will be }\$2.50\)
djdownfawl
New member
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- Sep 28, 2010
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Its telling me both answers are wrong.
djdownfawl
New member
- Joined
- Sep 28, 2010
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- 37
can somebody else please help me...
these answers are wrong...........
these answers are wrong...........
D
Deleted member 4993
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djdownfawl said:
You have been shown how to attack the problem.
Have you worked at it yourself?
If you didn't - do you think you deserve to get the credit for correct answer?
djdownfawl
New member
- Joined
- Sep 28, 2010
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I appreciate the help.
But FYI i only ask the problems the ones i am having issues with not the whole assignment.
Now can somebody please help me out here.
But FYI i only ask the problems the ones i am having issues with not the whole assignment.
Now can somebody please help me out here.
D
Deleted member 4993
Guest
But you are not answering the question I asked:
(After seeing the solution), have you worked at the problem yourself?
If the answer is "No", then my advice is - do it - and make sure you understand every-step.
Then in case the answer given to you has any type of "silly" mistake - you'll be able to catch it.
(After seeing the solution), have you worked at the problem yourself?
If the answer is "No", then my advice is - do it - and make sure you understand every-step.
Then in case the answer given to you has any type of "silly" mistake - you'll be able to catch it.