Problem Sets Optimization

1)    A cylinder, open on top, holds 100 liters of water. What is the circumference of this barrel, if it were made to use the least material?
2)    A company makes a block of cheese designed to have the height exactly five times the width. If they want a block of 1800 mm3, and using the least possible surface area, what would be the length?  

3)   What are the points on the curve y = x2 - 59/2 that represent the (local) minimum distances from the point (0, -4)? (Note: I have not shown you a problem like this before. The first thing you need to realize is that you need the distance formula. I asked you to minimize distance. The second thing is that in optimization problems like these, it is not necessary to draw a graph. They can be done entirely algebraically, without knowing what the hell you just did.)
Distance formula : (x - x1)2 + (y - y1)2 = D2



Copyright 2001 Bruce