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Quadratic Equation Application Word Problem : Maximizing and Minimizing Area

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A rectangular play yard is to be constructed along the side of a house by erecting a fence on three sides, using house wall as the fourth wall. Find the demensions that produce the play yard of maximum area if 20 meters of fence is available for the project.

What are the dimensions of an aluminum can that can hold 28 ounces of juice and that uses the least amount of aluminum? Assume that the can is cylindrical, and is capped on both ends.

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Solution Summary

Derivatives and quadratic equations are used to maximize and minimize area. The solution is detailed and well presented.

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  • 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"
  • "Thank you very much for your valuable time and assistance!"
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