Name: . Date: .
Optimization Activity
Materials:
Each group will need one sheet of white paper (dimensions are 21.6 cm by 27.9 cm), a pair of scissors, a ruler, tape and a sheet of graph paper.
You are at a party and as they are about to give out the loot bags filled with candy the host realizes that she has forgotten to buy bags. As a quick solution she gives each person a regular sized sheet of paper to build their own candy box! Use the sheet of paper provided to demonstrate the box you would make to put your candy in.
(Hint: Assume you like candy so you’ll want to maximize the amount of candy you can put in the box!)
To construct your candy box draw four congruent squares in each corner of your paper (see diagram below), the size of the four squares, x, is your decision. Using the scissors and tape, cut out your square and its corners to create an open-topped box.
Assignment: Complete the following questions:
1. The length of the cut-out square is ______
2. The width of my box is ______
3. The length of my box is ______
4. The height of my box is ______
5. The volume of my box is ______
A chart like the one below is on the board.
Add your data to the chart on the board and then copy the data from the chart on the board into your chart below.
x/height (cm) / Volume (cm3) / x/height (cm) / Volume (cm3)1. / 18.
2. / 19.
3. / 20.
4. / 21.
5. / 22.
6. / 23.
7. / 24.
8. / 25.
9. / 26.
10. / 27.
11. / 28.
12. / 29.
13. / 30.
14. / 31.
15. / 32.
16. / 33.
17. / 34.
9. Using the graph paper, construct a graph of x (height) versus volume by plotting the above ordered pairs.
Join the points with a smooth curve. Answer the following questions based on your graph.
10. What is the maximum volume? (According to your graph) .
11. What value of x (size of cut-out square) would result in the maximum volume? .
MCV4U-Optimization Activity Page | 3