Documentation:Math 104 Student Guide/Optimization/PracticeOptimization

From UBC Wiki

Sample Optimization Problems

Independent Problems

1. We need to enclose a field with a fence. We have 500 meters 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.

2. 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/meters^2 and the material used to build the sides cost \$ 6/meters^2. If the box must have a volume of 50meters^3 determine the dimensions that will minimize the cost to build the box.

3. We want to construct an equal sided box with a square base and we only have 10 m^2 of material to use in construction of the box. Assuming that all the material is used in the construction process determine the maximum volume that the box can have.

4. A manufacturer needs to make a cylindrical can that will hold 1.5 m^3 of liquid. Determine the dimensions of the can that will minimize the amount of material used in its construction.

5. A printer need to make a poster that will have a total area of 200 cm2 and will have 1 cm margins on the sides, a 2 cm margin on the top and a 1.5 cm margin on the bottom. What dimensions will give the largest printed area?


Problems from the Math Text Book

Calculus Early Transcendentals, Volume 1, Third Edition

Page. 261-267

Problems from the Math Exam Resources Wiki

December 2012 Exam Q3

December 2011 Exam Q3

December 2010 Exam Q4

December 2010 Exam Q5