Process

Make certain that each person consults the grading rubric and that it is understood exactly what is expected.

  1. Review the following steps used in solving Optimization problems.  They are as follows:
  2.  Recognition.  Recognize what type of problem it is.
  3. Read the problem.  Do not just look for the numbers and hope that they can be plugged in somewhere.
  4. Construct a diagram.  Sometimes drawing a picture makes solving the problem easier.
  5. Construct an appropriate equation and determine the interval
  6. Differentiate the equation, and
  7. Test the critical values and the endpoints of the interval to find the maximum or minimum.

These steps can be viewed in more detail by clicking here to take you to the website of Duane Kouba, a professor at the University of California at Davis.  There are also sample optimization problems with solutions.

For a tutorial of optimization problems click here to take you to the website of Paul Dawkins, a professor of Mathematics at Lamar University.

For sample optimization problems with animated figures showing how the optimization changes as the values change, click here to take you to the website of David Hill of Georgia State College and University. 

Other websites with opitmization problems can be found at you help you complete your tasks can be found by clicking the following: 

Analyze Math

Philippe Laval of Kennesaw State University

 

Task 1

Fortunately the treasure has been located and brought on board the salvage vessel.  Unfortunately the boat is out of gas.  The treasure must be brought to shore in a rowboat.  On board the boat is a large piece of metal measuring 16 feet by 12 feet.  If a square is cut out of each corner, and the resulting tabs are folded up, an open top box can be constructed. 

Determine the side of the square to be cut, so that a box with the largest volume can be constructed.  You want to be able to carry as much treasure as possible.

 

Task 2

The boat is 4 miles from shore.  The treasure is headed for a museum which is 10 miles from a point straight from the ship to the shore.

The person rowing the boat can row at a speed of 2 miles per hour.  Once on shore, the treasure will need to be carried to the museum.  It cannot be transported by motor vehicle, because here are no roads.  The people carrying the treasure can walk at a speed of 3 miles per hour.  At what point should they row to so that the treasure can reach the museum in the least amount of time?

 

Task 3

Congratulations.  The treasure has arrived safely at the museum.  The current attendance averages 6,400 people a week, but once the treasure is put on display the attendance will soar.

The current price for tickets at the museum is $20.00.  The head of the museum estimates that for each $2.00 reduction in the admission, the attendance will increase by 300 people a week.  What price should the museum charge to maximize their weekly revenue, and what will that revenue be?

When you have completed the above three tasks, hand your work in to the teacher.

 

Group Task

 

Create a Power Point presentation displaying the results and present it to the class.  Consult the rubric for requirements for the presentation.