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Optimization of a cylinder container with a height of 4 inches and a radius of 1.25...

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Physics

Optimization of a cylinder container with a height of 4 inchesand a radius of 1.25 inches in terms of either volume OR surfacearea.

Please provide:

(A) Calculation of surface area/volume of the container.

(B) Primary and secondary constraint equations

(C) Derivative of primary equation

(D) Optimized dimensions and how they were determined(number-line analysis to show that the dimensions result in anoptimized solution.

(E) Graph of optimization (in terms of volume OR surface area interms of the radius) marking the optimized value, as well as theactual value based on the actual radius.

(F) Comparison of your results with the container’s actual. Inother words, if you chose to optimize the volume, then show:Optimized volume-Actual volume/Actual volume×100%which shows the additional percentage of volume your optimizedcontainer holds. If you chose to optimize the surface area, thenshow: Actual surface area- Optimized surface area/Actualsurface area×100 which shows the reduced percentageof surface area your optimized container has.

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