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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.
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Is Feasible region is necessary to be a convex set?
Yes, in optimization problems, the feasible region must be a convex set to ensure that the objective function has a unique optimal solution. This is because convex sets have certain properties that guarantee the existence of a single optimum within the feasible region.
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 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.
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.
What is a concave face?
A concave face has a prominent forehead and a chin that is set back, creating a noticeable curve or dip along the profile of the face. This shape is often described as a "receding chin" or a "weak chin" in terms of facial structure.
If production set is convex then production function is concave?
correct.
Why do it possible to for a cave?
A real-valued function f on an interval (or, more generally, a convex set in vector space) is said to be concave if, for any x and y in the interval and for any t in [0,1],A function is called strictly concave iffor any t in (0,1) and x ≠ y.For a function f:R→R, this definition merely states that for every z between x and y, the point (z, f(z) ) on the graph of f is above the straight line joining the points (x, f(x) ) and (y, f(y) ).A function f(x) is quasiconcave if the upper contour sets of the function are convex sets.
Is the union of two convex sets a non-convex set?
the union of two convex sets need not be a convex set.
Is Feasible region is necessary to be a convex set?
Yes, in optimization problems, the feasible region must be a convex set to ensure that the objective function has a unique optimal solution. This is because convex sets have certain properties that guarantee the existence of a single optimum within the feasible region.
Why demand curve is convex?
Convex function on an open set has no more than one minimum. In demand it shows the elasticity is linear after some point and non linear on other points.
Is a circle a convex set?
no
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.
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.
Region enclosed by a circle a convex set?
Yes.
Is a ray a convex set?
no, because it should be a segment .
