# 3.2. Small Problems To Try¶

With exactly 2700 square inches of cardboard, we wish to construct a box (width

*2x*, depth*x*, height*2x*. We would like to maximize the volume*V*the box can hold. Which values of width, depth, and height fulfill our objective?A cylindrical can is to hold 20m

^{3}. The material for the top and bottom costs $10/m^{2}, and material for the side costs $8/m^{2}. Find the radius*r*and height*h*of the most economical can.A farmer wants to customize his fertilizer for his current crop. He can buy plant food mix A and plant food mix B. Each cubic yard of food A contains 20 pounds of phosphoric acid, 30 pounds of nitrogen and 5 pounds of potash. Each cubic yard of food B contains 10 pounds of phosphoric acid, 30 pounds of nitrogen and 10 pounds of potash. He requires a minimum of 460 pounds of phosphoric acid, 9060 pounds of nitrogen and 220 pounds of potash. If food A costs $30 per cubic yard and food B costs $35 per cubic yard, how many cubic yards of each food should the farmer blend to meet the minimum chemical requirements at a minimal cost? What is this cost?

“Travelling salesman problem”: Create a matrix of distances and then a row of nodes to go to and from. Use index to lookup the distance, and minimize the total distance.