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4.7B ITC Notes
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More Optimization Problems
Ex. Find two nonnegative numbers who sum is 9 and so that the product of one number and the square of other number is
maximized.
Ex. Find two nonnegative numbers where sum of the first number squared and the second number is 54and the product is a
maximum.
Ex. An open rectangular box with square base is to be made from 48 ft 2 of material. What dimensions will result in a box
with the largest possible volume?
Ex. A container in the shape of a right circular cylinder with no top has surface area 3 ft 2 . What height and radius will
maximize the volume of the cylinder?
Ex. A cylindrical can is to hold 20 m 3 . The material for top and bottom costs $10 / m 2 and material of side costs
$8 / m 2 . Find the radius and height that will minimize cost.
Ex. We need to enclose a field with a fence. We have 500 feet of fencing material and a building is on one side of the field
and so won’t need any fencing. Determine the dimensions of the field that will enclose the largest area.
Ex. We want to construct a box whose base length is 3 times the base width. The material used to build the top and bottom
cost $10/ft2 and the material used to build the sides cost $6/ft2. If the box must have a volume of 50ft3 determine the
dimensions that will minimize the cost to build the box.
Ex. A printer need to make a poster that will have a total area of 200 in2 and will have 1 inch margins on the sides, a 2 inch
margin on the top and bottom. What dimensions will give the largest printed area?
Ex. A farmer has 400 feet of fencing to make three rectangular pens. What dimensions will maximize the total area?
Ex. A printer need to make a poster that will have a total area of 150 in2 and will have 1 inch margins on the sides, a 1.5
inch margin on the top and bottom. What dimensions will give the largest printed area?
Ex. A cylindrical can is to hold 1m 3 . The material for top and bottom costs $10 / m 2 and material of side costs $9 / m 2 .
Find the radius and height that will minimize cost.