Answer to Question #326254 in Calculus for Max

Question

1. The sum of two positive numbers is 10. Find these numbers if the sum of their squares is a minimum.

2. Abby builds a rectangular pig pen with two parallel partitions using 150 meters of fencing materials. what should be the dimension of the pigpen so that it would enclose the largest possible area?

3. Find the dimensions of a rectangle with an area of 225 cm^2 whose perimeter is as small as possible.

4. Find two possible numbers whose the sum is 15 when the product of the first number and the square of the second number us to be a maximum.

5. The sum of two positive numbers is 18. Find the numbers if the sum of their cubes is a minimum.