1.Find two positive numbers that satisfy the given requirements. a. The sum of the squares of the two numbers is 48 and the product of the first times the square of the second is maximum.b.The second number is the reciprocal of the first and their sum is minimum.2.Applications a.Minimum surface area A box with a square base is to have a volume of 64 cubic inches. Find the dimensions of the box with smallest surface area.3.Cost of a Garden Fence A homeowner wishes to construct a rectangular garden with an area of 300 square feet that is enclosed by a low wall of landscaping stones. The cost per linear foot to construct the wall facing her house is $5. The cost per linear foot for the other three walls is $3. Find the dimensions of the garden for which the cost is a minimum.
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