Applied Optimization Problem (geometry/calculus) Please show all steps thoroughl

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Applied Optimization Problem (geometry/calculus) Please show all steps thoroughly!!!

A cylindrical can is to hold 40 pi in3. The material for the construction of both the circular top and bottom costs $5/in2 while the material for the construction of the side costs $16/in2. Write a function for the cost of this cylindrical construction. Note the following formulas: Area of a circle: A = pi r2, Area of the side of a cylinder: A = 2 pi rh and the Volume of a cylinder: V = pi r2h. Find the radius r and the height h which will result in the lowest cost of material. Justify that your answers from part b. result in a minimum cost.

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