SHOW YOUR SOLUTION.

Exercise 4.6 Optimization Problems: Applications of Maxima and Minima 1. Solve the following problems: 1. The sum of two numbers is 32. Find the minimum value of the sum of their squares. 2. The sum of two numbers is 18. Find the numbers if the product of one by the square of the other is to be maximum. 3. A cylindrical tank has a capacity of 350.53 m'. Find the minimum total surface area of the tank. 4. A right circular cone has a slant height of 7cm. Find the radius of the cone in order to have maximum volume. 5. A rectangular lot bounded by an already fenced side on its back is to be fenced. If the area of the lot is 10,000 m, what is the least amount of fencing that will enclosed the lot? 6. Compute the maximum area of a rectangle that can inscribe in an ellipse having an equation 9x# + 4y = 36. 7. A rectangular box with square base and top has a capacity of 10,000 em'. Find the height of the box that requires minimum amount of material. 8. From the figure below, compute for the minimum length of the wire used. 9. Find the height of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm. 10.A rectangular lot is to be enclosed by a fence. It has an area of 1 hectare. What is the least amount of fencing that will enclosed the lot having an opening of 2 meters in front