Math 151
Section 5.5
Applied Maximum and Minimum Problems
Example: Find two numbers whose difference is 65 and whose product is a minimum.
Example: Find the point on the parabola y = x 2 +1 that is closest to the point (3, 1).
Math 151
Example: A poster must have an area of 240 in2 with a 2-inch margin at the bottom and each of the
sides and a 3-inch margin at the top. What dimensions will give the largest printed area?
Example: A right circular cylindrical metal container, open at the top, must have a capacity of 192π
in3. The cost of the material used for the bottom of the container is 15 cents per in2. The cost of the
material used for the side is 5 cents per in2. If there is no wasted material, find the dimensions that
will minimize the cost of the material.
Math 151
Example: A person in a rowboat 2 miles from the nearest point, called P, on a straight shoreline
wishes to reach a house 6 miles further down the shore. If the person can row at a rate of 3 miles
per hour and walk at a rate of 5 miles per hour, how far along the shore should the person walk in
order to minimize the amount of time it takes to get to the house.
Example: Find the area of the largest rectangle that can be inscribed in
x2 y2
+ = 1.
4 16