Question: Solve the following optimization problems. Show your complete solution. Include an illustration of the problem if applicable. We are going to fence in a rectangular

Solve the following optimization problems. Show your complete solution. Include an illustration of the problem if applicable.

  1. We are going to fence in a rectangular field. Starting at the bottom of the field and moving around the field in a counter clockwise manner the cost of material for each side is $6/ft, $9/ft, $12/ft and $14/ft respectively. If we have $1000 to buy fencing material determine the dimensions of the field that will maximize the enclosed area.
  2. A cylindrical can is to be made to hold 1 L of oil. Find the dimensions (height and radius) that will minimize the amount of metal to manufacture the can. (clue: a cylinder can be made by sticking a circular and a rectangular metal sheet together)

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