An objective function combined with one or more constraints is an example of an optimization problem.
To solve optimization problems, we apply the method of Lagrange multipliers using a four-step problem-solving strategy.
Key equations
Method of Lagrange multipliers, one constraint
Method of Lagrange multipliers, two constraints
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints.
For the next group of exercises, use the method of Lagrange multipliers to solve the following applied problems.
A pentagon is formed by placing an isosceles triangle on a rectangle, as shown in the diagram. If the perimeter of the pentagon is
in., find the lengths of the sides of the pentagon that will maximize the area of the pentagon.
A large container in the shape of a rectangular solid must have a volume of
m
3 . The bottom of the container costs $5/m
2 to construct whereas the top and sides cost $3/m
2 to construct. Use Lagrange multipliers to find the dimensions of the container of this size that has the minimum cost.
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,