Minimizing Surface Area
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A container company is going to construct a shipping container of volume 12 ft3 with a square bottom and a square top. The cost of the top and sides is $2 per square foot and for the bottom is $3 per square foot. What dimensions will minimize the cost of the container.
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Solution Summary
Surface area of a container is minimized using derivatives. The solution is detailed and well presented.
Solution Preview
Assume that the length of each side of the square bottom is x. Assume that the height is y. Then we know that the volume is
x^2*y=12 ........................(1)
The cost is
...
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
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