CalcNotes Applied Optimization

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Section 4.6 Applied Optimization

Example 4.6.1.

Find the dimensions of the rectangle with smallest perimeter and area $100\text{~m}^2\text{.}$

Example 4.6.2.

Find the dimensions of an open rectangular box of maximum volume made from a sheet of cardboard 31 in by 17 in and created by cutting congruent squares from each corner.

Example 4.6.3.

A silo (without base) is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per square unit of surface area is 7 times as great for the hemisphere as it is for the cylindrical sidewall. Determine the dimensions to be used if the volume is fixed at 14000 cubmit feet and the cost of construction is to be minimized.

Example 4.6.4.

A small island is 6 miles from the nearest point $P$ on the straight shoreline of a large lake. If a dog on the island can swim 3 miles per hour and can run 4 miles per hour, where should she land in order to reach a town 14 miles from $P$ in the least time?