Find the two numbers whose sum is 74, and their product is as maximum as possible.
Find two numbers whose sum is and the sum of whose squares is the least possible.
What is the maximum volume of a right circular cylinder with surface area cm2? Give your answer in terms of .
Given that the volume of a hot air balloon grows according to the relation , where the time is measured in hours, determine its maximum volume.
A window is made of a semicircle on top of a rectangle, with the semicircle’s diameter equal to the rectangle’s width. Given that the window’s perimeter is 58 m, determine the semicircle’s radius that maximizes the window’s area.