detailed solution

EXERCISE Directions: Answer the following optimization problems systematically: 1.) Find the number in the interval (-3, 0] so that the sum of the number from its square is minimized. 2.) Find two numbers whose sum is 36 if the sum of their squares is to be a minimum. 3.) An open box is to be made from a 16 cm by 30 cm piece of cardboard by cutting- out squares of equal size from the four corners and bending up the sides. How long should the sides of the squares be to obtain a box with the largest volume? 4.) An open box is to be made from a 12 in by 10 in piece of cardboard by cutting-out squares of equal size from the four corners and bending up the sides. How long should the sides of the squares be to obtain a box with the largest volume? 5.) A poster is to have an area of 180 square inches with 1-inch margins at the bottom and the sides and a 2-inch margin at the top. What dimension will give the largest printed area