Sebastian wants to fence in a rectangular plot in a large field, using a rock wall which is already there as the north boundary. The fencing for the east and west sides of the plot will cost $3/yard, but he needs to use special fencing which will cost $5/yard on the south side of the plot. 9. W If the area of the plot is to be 600 square yards, find the dimensions for the plot which will minimize the cost of the fencing. Please round any decimals to three places. NORTH WALL (no fence needed) EAST WALL ($3/yard) AREA = 600 square yards WEST WALL ($3/yard) SOUTH WALL ($5/yard)
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
Sebastian wants to fence the rectangular plot. The fencing is not needed for north side.
The cost for fencing east and west sides is:
The cost for fencing south side is:
The area of the rectangular plot is:
square yards
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