A rectangular plot of land that contains 1500 square meters will be fenced and divided into...

 

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A rectangular plot of land that contains 1500 square meters will be fenced and divided into two equal portions by an additional fence parallel to two sides. Find the dimensions of the land that require the least amount of fencing. a. Draw a figure and label all quantities relevant to the problem. b. Name the quantity to be optimized and develop a formula to represent this quantity. c. Use conditions in the problem to eliminate variables in order to express the quantity to be maximized or minimized in terms of a single variable. d. Find a practical domain for this variable based on the physical restrictions in the problem. e. Use the methods of calculus to obtain the critical number(s). f. Test the critical number(s) to ensure it gives a maximum or minimum. g. Make sure the problem has been answered completely. A rectangular plot of land that contains 1500 square meters will be fenced and divided into two equal portions by an additional fence parallel to two sides. Find the dimensions of the land that require the least amount of fencing. a. Draw a figure and label all quantities relevant to the problem. b. Name the quantity to be optimized and develop a formula to represent this quantity. c. Use conditions in the problem to eliminate variables in order to express the quantity to be maximized or minimized in terms of a single variable. d. Find a practical domain for this variable based on the physical restrictions in the problem. e. Use the methods of calculus to obtain the critical number(s). f. Test the critical number(s) to ensure it gives a maximum or minimum. g. Make sure the problem has been answered completely.