3.4 Homework Day 2
For each problem: create your constraint, your max/min equation, substitute, and solve. You may also
want to draw the picture!
1. An open-top box is to be made by cutting congruent squares of side length x from the corners of a 24
x 24 inch sheet of tin and bending up the sides. Find the dimensions of the box that will maximize the
volume of the box.
2. Find two positive numbers whose sum is 36 and whose product is as large as possible.
3. Find the largest possible value of 2x + y if x and y are the lengths of the sides of a right triangle whose
hypotenuse is
5 units long. ( a 2  b 2  c 2 )
4. A cylindrical can is constructed using 100 square inches of tin. This amount also includes a top and
bottom for the can. What is the largest volume such a can might contain?