3.2. Small Problems To Try

  1. 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?

  2. 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.

  3. 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?

  4. “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.

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