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What does mean convex to the origin?
A set is said to be convex with respect to the origin if the line segment between any two points in the set lies entirely within the set. In simpler terms, for any two points within the set, all the points on the line joining them are also within the set.
Why is it that If production set is convex then production function is concave?
If the production set is convex, it means that any combination of inputs that produces a certain level of output can be formed by a convex combination of other input combinations. This implies that the production function exhibits diminishing returns to scale, leading to concavity. This concavity arises because as more units of an input are added, the incremental increase in output becomes smaller.
What is meaning of the convex?
Convex refers to a shape or surface that curves outward like the exterior of a circle. In mathematics, it describes a set where any line segment connecting two points within the set lies completely within the set. Convexity is often used in optimization and geometry to simplify problem-solving.
Can a convex mirror produce real images?
Yes, but it can be hard to arrange. You need to set up a real image as a virtual object, and make the convex mirror image that. If the rays converge strongly enough, they will still converge after reflecting off the convex mirror.
What is necessary for a convection cell to be set up in fluid?
A temperature difference within the fluid and a gravitational force are necessary for a convection cell to be set up. The warmer fluid rises due to lower density, while the cooler fluid sinks due to higher density, creating a circular motion known as a convection cell.
Region enclosed by a circle a convex set?
Yes.
What is the set of values that solve a system of equations called?
Depending on the context, the "feasible region" or "solution set".
Is the union of two convex sets a non-convex set?
the union of two convex sets need not be a convex set.
Is the set of all ordered pairs of real numbers that satisfy the system?
The feasible region is one possible anwer to this incomplete question.
Is a circle a convex set?
no
Is A union B a convex set?
yes
Is an empty half plane still a convex set?
The answer depends on how it is halved. If the plane is divided in two by a step graph (a zig-zag line) then it will not be a convex set.
What are convex polygons?
A convex polygon is one with no reflex angles (angles that measure more than 180 degrees when viewed from inside the polygon). More generally a convex set is on where a straight line between any two points in the set lies completely within the set.
Is a ray a convex set?
no, because it should be a segment .
Two lines with intersection is the empty set?
It can be if the set consists of convex shapes, for example.
If production set is convex then production function is concave?
correct.
What is optimal solution?
It is usually the answer in linear programming. The objective of linear programming is to find the optimum solution (maximum or minimum) of an objective function under a number of linear constraints. The constraints should generate a feasible region: a region in which all the constraints are satisfied. The optimal feasible solution is a solution that lies in this region and also optimises the obective function.
