AP Calculus Section 5.5
Applied Maximum and Minimum Problems
Homework:
Day 1
Day 2
Page 318 #1 – 15 odd
Extra Optimization Problems Handout
Objective: SWBAT use their knowledge of absolute max and min of a function in
order to solve real world optimization problems.
1. Five step procedure to solve applied max/min problems.
Step 1 Draw an appropriate figure and label the quantities relevant to the
problem.
Step 2 Find a formula for the quantity to be maximized or minimized.
Step 3 Using the conditions stated in the problem to eliminate variables, express
the quantity to be maximized or minimized as a function of one variable.
Step 4 Find the interval of possible values for this variable from the physical
restrictions in the problem.
Step 5 If applicable, use the techniques of the preceding section to obtain the
max/min.
2. A garden is to be laid out in a rectangular area and protected by a chicken wire fence.
What is the largest possible area of the garden if only 100 running feet of chicken wire is
available for the fence?
3. An open box is to be made from a 16-in by 30-in piece of cardboard by cutting out
squares of equal size from the four corners and bending up the sides. What size should
the squares be to obtain a box with the largest possible volume?
4.
An offshore oil well is located in the ocean at a point W, which is 5 miles from
the closest shore point A on a straight shoreline. The oil is to be piped to a shore
point B that is 8 miles from A by piping it on a straight line under water from W
to some shore point P between A and B and then on to B via a pipe along the
shoreline. If the cost of laying pipe is $100,000 per mile under water and $75,000
per mile over land, where should the point P be located to minimize the cost of
laying the pipe?
5. Find the radius and height of the right circular cylinder of largest volume that can be
inscribed in a right circular cone with a radius 6 inches and height 10 inches.
6. Find a point on the curve y  x 2 that is closest to the point 18,0 .